Jurgen Klopp’s side were totally in command of their last-16, first-leg tie in Portugal, where first-half goals from Sane and Mohamed Salah handed them a 2-0 lead at the break, before Roberto Firmino and the Senegal international completed the rout in the second half.
The hosts were poor in the first leg and were punished for committing errors at the back. They did create the first chance of the match in the ninth minute, however, when Moussa Marega set up Otavinho inside the box, but the Brazilian’s shot was deflected over the crossbar.
Andy Robertson tried his luck from distance on his Champions League debut in the 13th minute, but he failed to test Jose Sa with a rising strike. The opener arrived 12 minutes later, though, when Sa allowed Mane’s shot to squirm underneath his body into the right side of the goal.
The Reds doubled their lead just four minutes later as James Milner made his way into the box and looked to pick out the right corner of the net, but the ball came back off the post and Salah showed brilliant control to flick the ball over Sa before finishing from a few yards out.
Liverpool were in the driving seat, although the Dragons almost halved the deficit two minutes before half-time when Yacine Brahimi found Tiquinho inside the box, only for the Brazilian to miss the target with a low strike.
They were firmly on the back foot in the opening stages of the second half as the Merseyside giants extended their advantage from a clinical counter on 53 minutes. Firmino released Salah down the left with a backheel and received the ball back from the Egyptian before seeing his shot parried by Sa into the path of mane, who slotted home at the back post.
Loris Karius was called into action for the first time on 58 minutes, but Marega’s tame shot from the edge of the box was comfortable for the keeper.
Firmino converted another swift counter from the Reds 11 minutes later as he steered Milner’s square pass into the bottom-left corner of the net from 12 yards out.
After Mane missed the chance to complete his three-goal on 83 minutes with a shot on the stretch that went over the bar, the winger did manage to take home the match-ball when he beat Sa two minutes later with a scintillating strike from 20 yards out that flew into the right corner of the net.