Jurgen Klopp's side are the top scorers in this season's competition and they showed all of their attacking prowess as Mane, Mohamed Salah and Roberto Firmino put the tie to bed before the second leg at Anfield.
Mane opened the scoring after 25 minutes with the help of some questionable goalkeeping from Jose Sa, the Porto number one diving over his low shot after a driving run from Georginio Wijnaldum.
The visitors were two ahead before the half-hour as Salah made it 30 for the season, becoming the first Liverpool player to reach that figure since Luis Suarez in 2013-14.
Liverpool's attacking trident combined for their third goal and Mane's second after the break, and Firmino ensured all three got on the scoresheet with 21 minutes remaining.
There was still time for Mane to complete his hat-trick and effectively end any hopes Porto had of a second-leg recovery, with Liverpool's progression looking assured already.
4 - Sadio Mane is the fourth Liverpool player to score a hat-trick in the Champions League, after Michael Owen, Yossi Benayoun and Philippe Coutinho. Collection. pic.twitter.com/w3kteQwtDq— OptaJoe (@OptaJoe) February 14, 2018
A positive start from the hosts was nearly rewarded in the opening 10 minutes as Otavio wriggled free after good work from Moussa Marega, but Dejan Lovren did superbly to deflect his low shot over.
Liverpool's electrifying front three took time to click, with Salah wasting their first sight of goal with a misplaced pass for Mane inside the penalty area.
But they soon found their feet and in the space of four minutes Liverpool found themselves two goals ahead.
Sa gifted Mane the opener as he got his dive all wrong trying to save the forward's low shot, the ball creeping under his body and over the line – leaving the goalkeeper thumping the pitch in anger.
His frustrations were doubled four minutes later as Salah extended Liverpool's advantage, with the Egyptian juggling the loose ball into the net after James Milner's shot had thudded against the upright.
Porto should have reduced their deficit before the interval but Tiquinho Soares fired wide from Yacine Brahimi's beautifully weighted throughball.
That touch. That control. That man Mo! pic.twitter.com/dtI3C1JKnY— Liverpool FC (@LFC) February 14, 2018
If Porto had hoped that late chance would spark them into life after the restart they were left disappointed as Liverpool moved further ahead thanks to Mane's second.
After latching onto Salah's precise pass, Firmino's scuffed shot was well saved by Sa but the goalkeeper was unable to hold it and Mane coolly slid home the loose ball.
That seemed to finally bring the hosts into life but, as they chased the game, they were caught on the break by Liverpool's deadly trio.
Mane turned provider with a surging run and pass to Milner, the England international finding the unmarked Firmino to give him a deserved goal.
Liverpool were not finished there, either, as Mane completed his hat-trick with a fine solo run and shot from 20 yards – becoming the fourth Reds player to complete a treble in the competition.
Key Opta stats:
- Liverpool registered the joint-biggest away Champions League knockout win, equalling Bayern Munich’s 5-0 win at Sporting CP in February 2009 and Real Madrid at Schalke in February 2014.
- The Reds have scored more Champions League goals this season (28) than any other club.
- This is Porto's heaviest ever home European defeat and the first time they’ve conceded more than three goals in a home European match.
- Liverpool are the first English side to score five goals in an away Champions League knockout match.
- Sadio Mane is the fourth Liverpool player to score a Champions League hat-trick, along with Michael Owen, Yossi Benayoun and Philippe Coutinho.