Liverpool took the lead with 21 minutes on the clock when Roberto Firmino fired home.
Mohamed Salah then got in on the act when he finished on his weaker right foot.
The Egyptian then got his 50th Liverpool goal in 65 matches when he dispatched a penalty won by Sadio Mane.
The Senegal international later missed a penalty himself, hitting the bar.
The forward was on target in Saturday’s win at Huddersfield but has failed to show the same prolific form that saw him win the Premier League’s Golden Boot last season.
“Who? Who?” he joked.
“It’s great, I am happy to score my 50th goal for Liverpool, I am very proud about that,” Salah added.
“I want to keep scoring and help the team keep winning games.
“We know how to play with eachother, we know our quality and we are happy for eachother.”
Angel Di Maria scored an injury time equaliser for PSG against Napoli in the other Group C match meaning Liverpool now top it.
The Reds now host Cardiff City in league action on Saturday afternoon.
Neil Warnock’s side are fresh off the back of their first Premier League victory this season after beating Fulham last time out.