Liverpool's Mo Salah hit his 50th goal in the red shirt with his first converted Anfield penalty.
Klopp rings the changes
Jurgen Klopp had made five changes to the LFC team that edged over the line against Huddersfield. Joe Gomez was returned to centre-back in Lovren's place allowing Alexander-Arnold back into the side.
Fabinho and Gini Wijnaldum returned to the midfield, and up front both Sadio Mane and Firmino returned from injury and fatigue respectively.
Three points was a must for the reds against the Serbian champions, but for the opening 10 minutes it looked like this would be a real competitive game.
However, the reds soon had the measure of their opponents and the waves of attacks slowly began. Solidity in the middle from Fabinho, outlets of Shaqiri and Robertson, and the constant menace of Liverpool's front three.
Bobby breaks the deadlock
The opening goal was scored by Firmino. Shaqiri threaded a beautiful defence splitting ball to Robertson who whipped across for Firmino to tuck away.
A few minutes later Robertson fizzed over another cross that was half a yard ahead of the head of Mo Salah.
Andy Robertson arguably should have scored the games' second goal when Mane set him up inside the area but he drilled the shot over the crossbar.
Just before half time however it would be 2-0. Shaqiri, quickly becoming the Egyptian's new best friend, redirected a pass towards him and on his right foot he drilled in the goal.
Second half - no let up from the reds who raced out of the blocks.
Fabinho could have grabbed his first goal from the edge of the area but it would be Salah, minutes later, who would make it 3-0 with a powerfully struck penalty.
The award of the penalty was soft, but Sadio Mane did receive an arm across the face and for too long Liverpool have not been given these decisions.
Red Star began to lose their heads, they would eventually collect five yellow cards in total. It was playing into Liverpool's hands and both Daniel Sturridge and Adam Lallana, making substitute appearances, had opportunities to add their names to the scoresheets.
Mane gets his goal.. eventually
With 15 minutes left, the reds received another penalty. This time for handball. Mo Salah had been substituted off so Sadio Mane stepped up. His initial penalty was saved, but he made a mess of the rebound and it remained 3-0.
Fortunately he would get the goal he was looking for when he hit a sliding shot in just four minutes later.
With a draw elsewhere between Napoli and PSG - Liverpool move back to the top of Group C. There is still everything to play off and one of these three big sides will be dumped out of the competition. The reds win tonight puts them in the driving seat.