Mane was in the right place at the right time to score twice in the first half before rifling home his hat-trick just before the end, to overshadow the exploits of Salah, whose brilliant individual effort made him the second fastest to the 30-goal landmark in the club’s history and the quickest for 122 years.
Roberto Firmino also had an outstanding game and his goal — his seventh in Europe this season, with only Cristiano Ronaldo scoring more — was just reward for the Brazilian.
It ensured a comfortable night in the Estadio do Dragao as the Reds’ first knockout encounter in nine years at this level passed without major incident.
Liverpool’s 28 goals is more than anyone else in the Champions League this term, with 25 coming in their last five games.
It was only their third win in Portugal in 11 attempts but, if they were looking for omens on the two previous occasions — at Benfica in 1978 and 1984 — they went on to win the European Cup.
Asked if he considered last display the perfect performance, Liverpool manager Jurgen Klopp replied: “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.
I saw a lot of fantastic performances tonight, a result like this is only possible if they are all spot on. I think [Andrew] Robertson played an outstanding game, finally he found his crosses, I thought they were in Scotland or somewhere which was good to see. Of course Sadio [ is man of the match but Roberto Firmino’s work rate was outstanding again.”
Mane said: “Honestly it was not an easy game even if we scored five. We played great football from the beginning to the end.”
Paying tribute to Mane, James Milner said: “Sadio Mane does his job and does a great job for the team. People see his flair and the goals that he scores but he does a great job working for the team.
“Porto are a very good side. It’s a tough place to come, you could see the crowd and the way they were even at the end.
“We wanted to keep a clean sheet and with the players we have we always have the chance to score an away goal. I thought we could have scored more.”
Porto, without injured five-goal top scorer from the group stage Vincent Aboubakar, had won won 13 of their last 15 games and conceded just once in the last six, and the early signs were that they would be tough opponents.
A desperate lunge from Dejan Lovren deflected Otavio’s shot just over Loris Karius’ crossbar as a game of cat-and-mouse developed in the opening 20 minutes.
But with Liverpool dominating possession it was only a matter of time before a team with this firepower would find a way through.
When it came, in the 26th minute, it may have owed something to the conditions with rain swirling around the pitch as it had the city all day.
Georginio Wijnaldum’s pass reached Mane on the left of the area and his shot squirmed under Jose Sa despite the goalkeeper getting a hefty touch.
If that was the nerve-settler, the second goal was a cause for celebration, coming after James Milner cut in from the left and lashed a right-footed shot against the far post.
The lurking Salah was quickest to react, collecting the rebound, flicking the ball up twice with his left foot, nodding it on with his third touch and then forcing home from close range — all within the space of about five yards.
Former Liverpool captain Steven Gerrard, a half-time television pundit for BT Sport, offered the opinion: “If Lionel Messi did this, everybody in the world would be going crazy.”
It was the Egyptian’s ninth in his last eight matches, scoring in his last six games in a row, and only George Allan, whose 27 games in 1896 was seven faster than Salah, has reached the 30-goal mark quicker.
Liverpool were from then on able to control the game, although Yacine Brahimi cutting through their defence for Franciso Soares to fire just wide was a wake-up call seconds before the interval.
It was one they heeded as, after soaking up some early pressure, a quick counter-attack featuring an exquisite back-heel lay-off by Firmino to Salah — similar to his assist for the Egyptian’s goal at Southampton — in the centre-circle led to Mane tapping home his second after Firmino’s shot was parried by Sa.
The Brazil international finally found the target with 20 minutes to go as he side-footed home Milner’s cross before Mane’s piledriver put the tie surely beyond Porto.
Jose Sa, Ricardo Pereira, Reyes, Marcano, Alex Telles, Sergio Oliveira, Herrera, Marega, Otavio, Brahimi, Tiquinho Soares.
Karius, Alexander-Arnold, Lovren, van Dijk, Robertson, Milner, Henderson, Wijnaldum, Salah, Firmino, Mane.
Corona for Otavio 46, Waris for Brahimi 62, Paciencia for Tiquinho Soares 74.
Matip for Henderson 74, Ings for Firmino 79, Gomez for Alexander-Arnold.
Daniele Orsato (Montecchio).