Manchester United 1-2 Swansea City
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The hosting Red Devils had never previously been defeated at Old Trafford on the opening day of a Premier League season, having won eight and drawn three encounters before that.
Last season, Swansea won for the first time at Old Trafford in their history in the FA Cup and now they have broken their duck in league football.
Meanwhile, Wayne Rooney's goal for United was his 159th for the club, drawing him level in fourth place on United's all-time list of goalscorers with Dennis Viollet.
Leicester City 2-2 Everton
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The draw means that Leicester have won none of their previous six opening Premier League encounters, drawing four of them and losing two.
The match was Leicester's first as a Premier League club since they faced Arsenal at Highbury in May 2004.
Eight of the last 10 meetings between these two clubs in the Premier League have ended in draws.
Queens Park Rangers 0-1 Hull City
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Newly-promoted QPR are now without a win in 10 Premier League matches - a run that dates back to March 16, 2013.
In total, Harry Redknapp's men have won just four of their previous 40 outings in England's top flight.
As for James Chester, the goal that he scored was the 11th of his senior career and seventh in total for Hull.
Stoke City 0-1 Aston Villa
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Visiting Villa made the trip to the Britannia Stadium having failed to win any of their previous nine Premier League matches on the road.
The defeat was only Stoke's second in front of their own supporters since January 12.
Match winner Andreas Weimann found the net for the first time away from home since he scored at Anfield on January 18.
West Bromwich Albion 2-2 Sunderland
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The visiting Black Cats had only two shots on target at The Hawthorns, but scored with both of them.
Sebastian Larsson's last two goals in a Sunderland shirt have been scored away from the Stadium of Light.
Meanwhile, hosting West Brom have only failed to score in one of their previous 12 home matches.
West Ham United 0-1 Tottenham Hotspur
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Mark Noble had converted his last 10 penalty kicks, but he failed to hit the target against Spurs from 12 yards out.
New signing Eric Dier secured all three points for Tottenham, which ended a run of three straight defeats against West Ham in all competitions.
The match marked Sam Allardyce's 400th in charge as a Premier League manager.
Arsenal 2-1 Crystal Palace
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Arsene Wenger's Gunners won for the first time on the opening day of the campaign since they thrashed Everton back in 2009.
The late victory, secured by Aaron Ramsey, was the 100th triumph that Arsenal have had in the Premier League at the Emirates Stadium.
Palace defender Brede Hangeland, who had gone three Premier League seasons without scoring for his former club Fulham, found the net on his Eagles debut.
Liverpool 2-1 Southampton
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Daniel Sturridge's goal was his 36th in 50 outings for Liverpool. That is a better return than the likes of Luis Suarez, Robbie Fowler, Ian Rush and Kenny Dalglish all managed over the same time period.
Liverpool's other goalscorer - Raheem Sterling - has now found the back of the net in his last two outings against Southampton.
The Saints have won just one of their last eight opening-day Premier League matches.
Newcastle United 0-2 Manchester City
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No defending Premier League champion has ever lost the opening game of the next campaign and City continued that sequence at St James' Park.
Sergio Aguero, who scored the second goal, has now been directly involved in 24 goals in his last 24 City appearances.
The hosting Magpies have failed to find the net in their last four outings against the Citizens.
Burnley 1-3 Chelsea
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The Blues are unbeaten since the 1998-99 season in their opening Premier League game.
Last season, it took until New Year's Day for a Chelsea striker to score a goal away from home. Yesterday, it took summer signing Diego Costa just 17 minutes to find the back of the net.
Burnley have conceded 15 goals in their last four home Premier League encounters.