Roma scored two goals in the final nine minutes to just about keep their Champions League semi-final tie with Liverpool alive, although they still have a 5-2 deficit to overturn in next week's return match.
The Reds took their tally in this season's competition to 38 goals with five more in a rampant display at Anfield, which was somewhat soured when they switched off late on to concede twice.
Mohamed Salah was the star performer against the side that sold him last summer, scoring two and setting up two more of Liverpool's five goals on the night, but Edin Dzeko's late strike and a Diego Perotti penalty ensured that it is not quite tie over for the Giallorossi.
The tempo was set right from the first few minutes when Kevin Strootman side-footed his shot down the throat of Loris Karius, while up the other end man of the moment Salah cut inside and gave Alisson something to think about.
Roberto Firmino got in behind two minutes later but could not pick out a teammate with his fizzed delivery, and Alex Oxlade-Chamberlain sent the next shot right at Alisson just like Salah before him.
The shoot-on-sight policy continued as Radja Nainggolan tried his luck with a wayward effort, but the end-to-end feel to the match halted just short of a quarter of the way through following an injury to Oxlade-Chamberlain, who had to be stretchered off the field in a blow for club and country.
Liverpool's slight reshuffle, with Georginio Wijnaldum filling in, allowed Roma to take control of the match for the next 10 minutes.
The Giallorossi's controlled possession culminated in a rocket of a shot from Aleksandar Kolarov, which Karius managed to get a touch to and help it on to the crossbar.
In the blink of an eye momentum was soon back with Liverpool and, unlike their opponents, they would make it count.
Sadio Mane wasted two decent openings, sending the best of them over the bar when played through, while Salah's curler was well dealt with, but the next time the Egyptian cut inside on his left it was a different story.
All Alisson could do was pick the ball out of the back of the net after Salah's shot was sent curling past him via the frame of the goal - the forward's 42nd goal of the campaign being greeted with an apology more than a celebration against his ex-employers.
Liverpool, who also had a Mane goal ruled out for offside and hit the crossbar through a Dejan Lovren header in a frantic spell, were two in front before the break thanks to Salah's second, this time lifting the ball over Alisson 12 seconds after Virgil van Dijk cleared a corner to spark a counter.
Roma have recovered from first-leg defeats in both knockout rounds, most memorably beating Barcelona 3-0 on home soil last time out, but damage limitation appeared to be the order of the day for Eusebio Di Francesco in the second half.
Those plans lasted all of 10 minutes, however, as Salah turned provider by squaring the ball to Mane to make amends for his earlier misses with a simple finish past Alisson.
Di Francesco's use of wing-backs high up the field was proving to be a disaster, as Salah was left in acres of space down the right for a second time and this time laid the ball on for Firmino to tap in from all of a yard.
If the previous four were well worked in their own right, the fifth goal could not be put in that category as Firmino simply got his head to a corner and guided it past Alisson, taking advantage of the terrible zonal marking.
Jurgen Klopp had the luxury of taking off Salah with 15 minutes left to play, resting him for what at this stage appeared to be a dead rubber return leg in a little over a week's time at the Stadio Olimpico.
Roma, with just two defeats in their previous 11 away matches, then came close to pulling one back through a saved Patrick Schick header.
An incredible finale to the match saw the Giallorossi salvage more than just pride, though, as Dzeko chested down a searching Nainggolan pass and thumped it past Karius, before Perotti tucked away from the penalty spot once James Milner handled inside the box.
LIVERPOOL (4-3-3): Karius; Alexander-Arnold, Lovren, van Dijk, Robertson; Oxlade-Chamberlain (Wijnaldum 18'), Henderson, Milner; Salah (Ings 75'), Firmino (Klavan 93'), Mane
ROMA (3-4-2-1): Becker; Fazio, Manolas, Jesus (Perotti 67'); Florenzi, De Rossi (Gonalons 67'), Strootman, Kolarov; Under (Schick 46'), Nainggolan; Dzeko
Daniel Lewis
