On a wet and windy night at the Estadio Dragao, Jurgen Klopp’s side withstood the early Porto storm to give themselves a first leg advantage and one step into the next round before they return to Anfield next month for the second leg.
Despite the early pressure from the hosts, it was Mané who opened the scoring after 25 minutes as the visitors begun to grow into the game.
Georginio Wijnaldum charged into the Porto box but his shot was blocked and the Dutchman regained possession. He slid the ball to Mané and his tame shot wriggled under the gloves of José Sá to give the Reds the lead.
Salah doubled the lead five minutes later as he latched on to a James Milner effort that had rebounded off the post.
Sumptuous follow-up ball control allowed the Egyptian to juggle the ball over the outrushing Sá and prod home into the back of the net.
It was the Senegalese forward who would add to the Reds lead early into the second half. Salah played a ball into Roberto Firmino but before the Brazillian could add his name to the scoresheet, he saw his effort parried away by Sá.
However, the 'keeper could only push the ball out as far as the waiting Mané who stroked home comfortably.
Firmino would eventually get himself on the scoresheet as he swept home from Milner's low left-hand side cross at the halfway point of the second period.
Mané would have his hat-trick when he rocketed in his third with, a handful of minutes remaining, from outside the 18-yard-box past an outstretched and comfortably beaten Sá.
Porto press early but Reds patience pays off
Yacine Brahimi had Trent Alexander-Arnold on his heels twice inside the first five minutes but on either occasion, the winger couldn’t find a teammate in the box and instead had to settle for a corner.
All of the games early pressure came from Porto, Otávio with the best chance. He fired at goal but saw his shot deflected over the bar. The resulting corners led to a headed effort for Hector Herrera but that was comfortably caught by Lorius Karius.
It took 20 minutes for the travelling Reds to grow into the game.
Salah almost capitalised on a horrendous clearance from Porto ‘keeper José Sá but his cutback to the arriving Roberto Firmino was cut out by Iván Marcano.
The Egyptian caused trouble moments later but he was unable to find an unmarked Mané with his low cross avoiding the outstretched Diego Reyes.
He and Mane would find the net moments later.
The Primeira Liga leaders had a golden chance to cut into the deficit on the stroke of half-time but Tiquinho Soares fired wide of Karius’ post.
Visitors make fast second-half start and wrap up tie
Unlike the first 45 minutes, Liverpool began the second period in quick fast with Mané adding to the lead with the visitors' third goal of the night and his second.
If the game, and possibly the tie, wasn't wrapped up there then Firmino's finish before the 70-minute mark certainly finished off proceedings.
The hosts had a shout for a penalty waved away by referee Daniele Orsato but unlike the first period, they were unable to truly trouble the Liverpool backline.
Lorius Karis, who said in the build-up to the game that his job is to step-up when his defence is in trouble, was merely a spectator.
The German made two saves in the first 80 minutes and was rarely troubled.
His job was made even easier when Mané completed his treble for the night and grabbed Liverpool's third in the dying embers of the game.
Dragons require a miracle
Sérgio Conceição's side will require a miracle when they travel to Anfield at the beginning of March if they want to qualify for the Champions League Quarter-Finals stage.
His Porto team started well against the Reds but ultimately faltered once Klopp's side took the lead.
Their Champions League campaign is more than likely over but will almost certainly travel to Merseyside hoping to salvage a modicum of pride.