The Belgian forward did not know a great deal about the close-range finish, which came about after Steven Naismith's cross into the box was parried directly into his path by Julian Speroni.
Palace looked lively at times for the remainder of the first half, but they were unable to create any real chances of note following the restart as the Toffees picked up a first win in nine outings.
Relive how the events in South London unfolded with Sports Mole's live text coverage below.
The form of these two sides could not be more contrasting coming into this fixture, with the hosts enjoying a rejuvenated spell under new manager Alan Pardew, while their opponents have taken just two points from the last 18 on offer. Locked on 23 points apiece, victory for either team here today will see them close in on a place in the top half of the table.
So fresh from their mid-season break to Doha (lucky for some, eh?!), Everton have something close to a fully fit squad to call upon for this afternoon's meeting. However, James McCarthy - who has been strongly linked with a move to Tottenham this January - is not part of the matchday squad, although Darron Gibson is fit enough for a place among the substitutes.
John Stones joins Phil Jagielka in the heart of defence for the visitors, meanwhile, but there appears to be some question marks over the fitness of Ross Barkley who is not a part of the starting XI. Romelu Lukaku is tasked with leading the attack with Steven Naismith seemingly alongside him in a 4-4-2 formation.
As far as the home side are concerned, recent signing Jordon Mutch fails to make it into the starting lineup, while Shola Ameobi is still lacking in match fitness following his move on a free contract this week. Another January recruit in Yaya Sanogo retain his place up top alongside Dwight Gayle, meanwhile, as Palace look to keep up their impressive form in 2015.
Jerome Thomas misses out having picked up a knock recently, with Joe Ledley and James McCarthur tasked with filling in the middle of the park. Maurouanne Chamakh and Jason Puncheon are also handed starting spots in what is a strong looking Eagles side this afternoon.
As already touched on a little earlier, Palace can call on former Cardiff City and Queens Park Rangers midfielder Jordon Mutch from the bench this afternoon should they need some additional box-to-box power in midfield, while two of his former Bluebirds teammates in Fraizer Campbell and Wilfried Zaha are also on the bench from the off here today. In terms of Everton's back-ups, they have Barkley among their subs - the only alteration from last time out - with the energetic Bryan Oviedo also part of the matchday squad.
So three changes in all for Palace then, as they look to maintain their winning start to life under manager Alan Pardew. The former Eagles player admitted upon taking the job that he finally feels at home in his surroundings, and that is clear to see with four wins from four in league and cup competitions. What has pleased Palace supporters most, though, is the resilience shown by their side in battling from behind in both Premier League victories under the new man in charge.
It is clear to see that Pardew has also been given full financial backing, highlighted by the purchase of Mutch this week from QRP, which should help the former Newcastle United boss turn Palace into an established top-flight outfit in the years to come. Of course, things looked a little bleak just a month or so ago with the South London outfit struggling in the bottom three, which saw them installed as one of the bookies' favourites to face the drop.
In fact, Pardew's Newcastle team edged out Everton in his last game in charge at St James' Park, at which stage Palace were camped inside the bottom three, six places and five points behind today's opponents. That was then. A sustained run of poor results from the Toffees since, coupled with the Eagles' ability to get stuck in and pick up some positive results of their own, has seen this fixture take a completely different outlook.
That said, the task has still got to remain the same for Pardew this season - avoid relegation and push on next term. Some may dismiss 'second season syndrome' as nothing other than a myth, but go back to the inception of the Premier League in 1992 and it is clear to see that the big challenge for promoted teams is staying in the top flight beyond their second campaign at this level. If recent weeks are anything to go by, particularly that gutsy 3-2 FA Cup triumph over Southampton last time out, then the Eagles certainly have nothing to worry about between now and May.
If the target for Palace this season was to simply remain in the division, then things couldn't have been much different for this afternoon's opponents. Having narrowly missed out on a place in the Champions League, Everton had to make do with a place in Europe's secondary competition - the Europa League. There is no question the additional games and gruelling Thursday-Sunday schedule has had an effect on the Toffees, who are sitting just four points above the drop zone coming into this one.
It could be argued that it says more about Everton's current plight than the Eagles strong run of form that these two sides are currently level on points, with just two points taken from a possible 18 and no win in six league outings highlighting just how bad things have been for the Merseyside club of late.
Roberto Martinez will be hoping that this week's training camp in Doha will help put a spring into his players' step, with a mini mid-season break perhaps the idea catalyst to kickstart his side's campaign once and for all. It's hard not to be too disheartened if you're of an Everton disposition, however, as the club sits a massive 17 points off the top four. A place in the latter stages of the Europa League offers some hope, but defeat here today and make no mistake about it, a relegation battle reallt could be on the cards.
Sitting on 23 points from their 22 games (I won't insult you by pointing out that's only slightly better than a point-a-game ratio), Everton currently have their lowest tally since 2000-01 - a season which saw them finish in the lower reaches of the table. The good news? Three points today could see them close in on the top half, and with plenty of games still to come, a late charge for a top-six finish is certainly not off the cards in what is a strange Premier League season.
DID YOU KNOW? Palace have the worst home defensive record in the Premier League this season, conceding an average of 1.5 goals-per-game thus far. They come up against an Everton side who have themselves surprisingly struggled at the back throughout this campaign, keeping a joint-low four clean sheets.
PREVIOUS MEETINGS: The Eagles have come out on top in the last two meetings between these two sides, winning both games 3-2 at Goodison Park. However, that goes against the trend as Palace have only actually won one of their five games against the Blues at their Selhurst Park home in the Premier League, losing three of those contests.
Elsewhere in the Premier League this afternoon, Newcastle United have inflicted a heavy 3-0 defeat on strugglers Hull City at the KC Stadium. Victory for the Tigers, who are currently inside the bottom three, would have seen them move to within one point of both Everton and Palace, although the gap between the bottom three now remains at four points.
To put that into some context, Newcastle in 10th place sit seven points above these sides, so there is certainly a bit of a rift opening up between the top and bottom half of the table.
PREDICTION: Right, I hope I've done enough to whet the appetite ahead of this afternoon's clash at Selhurst Park, and with kickoff a little over five minutes away it's time to offer a prediction for how I see this one panning out. Of course, the form of the two sides is certainly contrasting coming into the game, but it's difficult to completely rule Everton out. That said, Pardew has worked his magic at a place he calls home, so with that in mind I'm going to back a 1-1 draw.
Okay, both teams are now out onto the field with kickoff just seconds away now. This should be an entertaining contest between two sides who are looking to push into the top half of the table with one eye over their shoulder. Three points will make a big difference for both sides, as the Selhurst Park crowd up the pre-match volume levels.
Dream start for Everton, who take the lead inside two minutes in South London. Naismith was able to get in around the back of the Palace backline before firing a cross across goal which the returning Julian Speroni could only parry into the path of Lukaku. The Belgian didn't know an awful lot about it, but he tapped it home for his first Premier League goal in nine outings.
OFF THE LINE! What an frenetic start! Gayle latched onto a hopeful ball forward which he brilliantly flicked over the advancing Joel, but Jagielka raced back to clear off the line. Great response from Palace, who are looking to level following that early setback.
The resulting corner causes panic at the back for Everton, and following a half-hearted clearance Sanogo lashed the ball goalwards on the volley only for Stones to clear away near the line once more. Palace have fought back in their last two league outings, and the early signs are that they will do likewise here again.
A chance for a little breather at last following that barnstorming start. It's the home side who are seeing more of the ball, but unable to really create any openings other than that little spell of early pressure shortly after falling behind.
Everton do not look convincing at the back at all as they just about clear away another set piece. I'm willing to bet that they will not keep a clear sheet this afternoon.
SHOT! Chamakh, fresh from his two-goal showing at Southampton last week, does brilliantly to control a ball on the edge of the box and work some space. He eventually fires away a shot which is blocked away by Stones. Vital interception by the Englishman, because that looked to be heading for the back of the net.
That early Lukaku goal is still the difference as we enter pass the quarter-of-an-hour mark at Selhurst Park. Palace have certainly had the better of things since that point, but the Toffees have just about managed to clear away everything that has come their way so far.
Everton earn a free kick in a promising position within shooting range of goal, and there is no surprise that Leighton Baines is the man who quickly jumps onto the ball. He will perhaps wish that he hadn't, though, because the effort was rather poor in the end.
Joel collects a cross into the box, which will do his confidence a world of good, and his throw out to Lukaku springs a potential Everton counter. A fantastic sliding tackle from Delaney puts paid to those hopes, however, and it is Palace who have possession once more.
A concern for Palace now as Chamakh is down on the field receiving treatment following a collision in the Everton area. His nose appears to be heavily bleeding, so unless that can be stemmed his afternoon will be over.
Incidentally Coleman, the other man involved in the clash of heads, is fine having shaken it off. A stretcher is now on the field for Chamakh who came off second best, so play will be held up for a little while longer.
That injury took up about five or six minutes of play, so there will be a fair bit of time added on at the end of the half. More immediately, the Eagles will be looking to rebuild some momentum before the break.
Everton have faired better since play resumed as they look to build on their advantage. Lukaku picked out Naismith on the edge of the box to allow the Scotland international to get a shot away, but he got right behind it and the ball is still rising now.
Some delightful build-up play from Everton begins with Barry working the ball out of midfield, playing it into the feet of Mirallas who in turn finds Baines on the overlap, but the full-back overhits his cross into the box. Good spell from the Toffess.
Ledley has done well this afternoon keeping things ticking over in midfield, and on the whole Palace have dealt well to deal with Everton's attacking threat. Incidentally, Australia international Jedinak could feature next weekend having ended his Asian Cup campaign earlier today with victory over South Korea in the final on home soil.
SAVE! Fantastic effort from Puncheon, who picks up the ball some 40 yards from goal before pushing forward and firing away, but the stop from Joel was equally as impressive down low. He pushed the ball behind for a corner, ensuring that Everton still hold onto their slender advantage.
Ledley picks out Puncheon inside the opposition area, but he was unable to get hold of the ball as Everton clear away. There's a nice feel to this game at the moment, with Palace looking the better of the two sides overall.
Wales international Ledley is involved again, losing the ball before winning it back from Lukaku, but Palace's attack breaks down when Mutch's cross from the right is blocked at the first man. The game is opening up as Everton burst forward before seeing their own attack peter out.
CHANCE! Both sides have made some defensive mistakes in the opening 42 minutes or so, although neither have really been punished for their failings thus far. The latest opening was all about Lukaku, though, but when left one-on-one with Delaney he over hit the ball as he raced through on goal, which was subsequently cleared away. You would expect him to do better when left in that type of position.
Gayle wins his side a corner, their fourth of the afternoon, but like before it is all too easy for Joel who collects with ease. The fourth official has just indicated that we will play an additional five minutes of added time at the end of this first half, following that injury picked up by Chamakh.
Everton are the side asking the questions as we enter the closing stages of the half, but their spell of pressure ends when Lukaku swings a cross out of play.
SHOT! Puncheon opts to shoot from the edge of the box, and despite having to bend his body to get away the volley, it wasn't a million miles away from target in the end. Decent enough effort, yet Palace know that more is needed in the second half.
Romelu Lukaku was the man in the right place at the right time to capitalise of Naismith's drilled cross which was parried into his path by Speroni, although it has arguably been the home side who have boasted the best chances since that point and they will feel aggrieved to be behind at the interval.
Gayle saw his hooked effort saved off the line by Jagielka, while his central defensive teammate Stones was needed to clear away Sanogo's volleyed attempt which also appeared to be heading for the back of the net. The only other real attempt of note came via Puncheon who tested Joel from range, although the Spaniard was equal to the shot to push it behind.
Everton have played some nice football at times, but the end product has too often been lacking. Naismith was picked out on the edge of the box by Lukaku before firing over, while the Belgian failed to make the most of a one-on-one opening at the back when left up against a tracking defender. That ensures that we are all level at the break with 45 minutes still to play in South London.
Romelu Lukaku has now scored 39 goals in 89 Premier League games since the start of the 2012/13 campaign. pic.twitter.com/6cPWnjuVLw
— Squawka Football (@Squawka) January 31, 2015
A nice spell of pressure from the Eagles in the opening stages of the second half soon fizzes out when Delaney concedes a free kick. It is worth noting that Pardew chose to bring Mutch on in that first half when he has Zaha on the bench, meaning that he is still fielding a forward in a wide position.
Both sides need to up things at the moment with the game just ticking along without a great deal happening. There's a good atmosphere inside Selhurst Park, but so far the Palace players have been unable to respond.
Everton have kept just four clean sheets this campaign remember, which remains a joint-low in the league, yet they are on course to extending that particular statistic. On the other side of the coin, no side has conceded more goals in front of their own fans than Palace.
Barry is limping along at the moment with Barkley watching on from the bench. Everton can also call upon Kone should they opt to go more attacking, while Palace, chasing a goal, have Zaha on the substitutes' bench.
The slow start to this second half stretches into its 11th minute with neither side able to create any openings of note. Expect that to change with Palace needing to find a goal. Jordon Mutch looked to create something from the right with his cross into the box, but it was all too easy for Stones to head away.
Half a chance for Sanogo perhaps, who fails to get his head onto a decent cross into the box which sails straight out of play. He looked to be slightly offside anyway, so Everton will be pleased that nothing came of that.
Palace have enjoyed a sustained spell of pressure, but in fairness Everton don't look all that troubled at the back. Pardew has surely got to start thinking about making a change right about now?
The hosts spring another counter which once more breaks down around the opposition box. It has been a sluggish opening quarter to the second half, which shows now sign of changing until a substitution is made.
A long ball over the top almost pays dividends for Palace, but Joel raced out to bravely head the ball away. Zaha appears to be coming on for the Eagles now during this short pause in play, while Everton also look likely to change things up. Thank goodness!
Gayle was almost in around the back for Palace, but Stones was covering across to clear away and deny the forward a strike on goal. Incidentally, Ledley appears to be playing at left back now with Sanogo remaining on that wing. Zaha is likely to be given a roaming role.
EVERTON SUB: Oviedo has been introduced in place of Mirallas, who has not done a great deal this afternoon. Martinez was waiting to weigh up the Palace changes before making his move, and he has now done so by bringing on the energetic Costa Rican.
Still absolutely nothing to report back as far as chances are concerned, which will suit Everton just fine. It is they who lead thanks to Lukaku's early goal, and with time fast running out the hosts cannot find the quality needed in the final third to find a way through.
Everton face Liverpool and Chelsea in their next two games, so this really would be a massive result for them if they can see it out. Palace have now made all three chances, so with 15 minutes left to play there is not a great deal that Pardew can now do. His winning run as Eagles boss appears to be coming to an end.
Jagielka has had a solid game so far and it is he who blocks away Murray's attempted cross into the box. This contest may be delicately poised, but this second half really has been poor.
Palace have scored 12 goals in four games under Pardew so far, but they haven't looked like scoring until for the best part of an hour. Eight minutes to go at Selhurst Park.
Crystal Palace are having to take risks now which is opening up some space at the back for the Blues to attack into. Naismith almost capitalised on this only for his shot to be blocked, before he was disposed by McCarthur when in behind the defence.
SAVE! A big save from Speroni to keep his side in the game. McGeady tried his luck with a curling effort which was heading for the back of the net if not for the interception of the Argentinian stopper. It was not quite in the corner, yet it was an impressive save nonetheless.
SHOT! This game has finally come to life with just a few minutes remaining, and it is another chance for Everton. Lukaku blasts an effort into the side-netting when in atright position inside the area, as another opportunity goes begging for the visitors.
Everton are just four minutes of added time away from bagging a rare away win - their first in three months - and just a fifth clean sheet of the season.
Delaney launches a hopeful ball long, but Murray concedes a free kick to the relief of Everton's travelling support. That signals a mass exodus with just 60 seconds left to play. Incidentally, Baines was shown a yellow card for dissent a few moments ago.
Ward had to be on guard to turn a ball away with Kone closing in on goal. Everton appear to have done enough to grind out victory with time officially up in South London.
Referee Roger Eats signals the end of the game, ensuring that Everton pick up a first win in nine outings. Lukaku's goal inside the opening two minutes proved to be the difference, as the Toffees ground out just a fifth clean sheet of the season to take all three points from South London.
Well that's all from me for the time being in terms of live commentary, but be sure to stick around as we bring you a full match report, player ratings, analysis and all the reaction from Selhurst Park.
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