And Liverpool was left reeling when Mohamed Salah misplaced a pass that allowed Neymar to carry the ball forward and Mbappe to produce the equaliser. As the PSG players wanted an offside call, Sturridge dove to play the ball after his heavy first touch.
6 minutes later, James Milner doubled the lead for the Merseyside Reds from the spot.
While Liverpool found a late victor, questions have already been asked about the play of PSG star Neymar. He looks bored, disinterested.
Even manager Jurgen Klopp admitted he thought the 26-year-old had "no chance" of playing when he saw him on Monday, but Mane was not prepared to give up on his team-mate. We're still waiting for that to happen.
The forward has scored his 12 goals in 16 matches and at his current strike rate of 0.75 per game, Firmino would require another 24 Champions League outings to catch Kop icon Gerrard.
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Liverpool showed last season, though, that they possess the ability to outscore virtually every opponent, and they repeated that against PSG, who once again appear too open at the back to make a genuine run in the knockout stages.
Klopp claimed after the match that they targeted Neymar's flank knowing he isn't a great defender. But at PSG, he is just an expensive decoration. Scotland worldwide Robertson has become one of the best left-backs in Europe since arriving from Hull City for £8m just over a year ago, and it was his cross that teed up Sturridge's goal on 30 minutes.
PSG had battled back from two goals down at Anfield and appeared on course to secure a draw in their opening game in Group C. Motivation is easy for Mbappe, but it is less so for Neymar, and the frustrations of playing for a PSG team that can not compete against the best in Europe looks to be blunting his edge.
Milner got the Anfield crowd going with a hard, but fair tackle on Neymar during the first half.
Jordan Henderson might not be the most glamorous player in history but his attitude and desire to work hard have kept him at the club as long as he has been.
However, Crooks seems to be convinced that the Reds will be Manchester City's closest challengers for the Premier League title this season. It doesn't look like he has that right now, though, and it was there for all to see at Anfield.