A hat-trick from Sadio Mane, and goals from Mohamed Salah and Roberto Firmino, rounded out a convincing victory that all but seals Liverpool's place in the quarter-finals for the first time in nine years.
In his pre-match comments, Jurgen Klopp reminded the press that Mane shouldn't be forgotten behind Salah and Firmino.
Salah then scored a delightful goal just four minutes later, his 30th of the season.
Mane had his second shortly after half-time by finishing off a typically venomous counter-attack.
Firmino put the game out of reach with 21 minutes remaining when he finished off James Milner's square ball.
Mane rounded off his first hat-trick for the Reds on the 85th minute mark with a rasping long-range strike.
Asked if the win was perfect, Klopp said: "Yes. You could say that of course. It was very professional, very mature in the right moments, very aggressive, good defending, good counter-attacking, keeping the ball, moving them around. In this game it was possible, usually it's not that easy.
"It was hard work but at the end the boys enjoyed the work and that's the most important thing."
The second leg will take place at Anfield on March 6.