The win leaves Jurgen Klopp's side on the verge of qualification for the Quarter-finals.
Story of the game
The first-half was a pulsating affair despite a lack of goals.
Inter's Lautaro Martinez had the first real chance within the first five minutes, but he curled his effort wide of the post from range.
Mané then fired an overhead kick into the side netting after the Inter defence had stopped for a possible foul in the 23rd minute.
Trent Alexander-Arnold had chances either side of the half hour mark, his free-kick curled narrowly past Samir Handanovic's post before he smashed a shot into the crow from range.
The Italians began to work their way back into the game but were frustrated by Virgil Van Dijk and Konate several times.
Milan Skriniar ought to have done better when rising highest from a corner with five minutes of the half to go.
Roberto Firmino replaced Jota after the half-time break.
The home team started the second-half with the better intensity, and Martinez should have gave them the lead after 53 minutes, but he failed to reach Ivan Perisic's cross.
With 60 minutes gone, Dzeko thought he had broken the deadlock but the Liverpool high-line caught him offside.
Diaz nearly had an instant impact, a one-two with Alexander-Arnold saw him free in the box, but Handanovic was quick to react.
At the other end, Denzel Dumfries escaped his marker from a 73rd minute corner and powered his header just over the crossbar.
With 15 minutes to go, the Reds took the lead, Firmino met Robertson's corner at the near post and his header looped into the bottom left corner.
Perisic nearly restored parity in the 80th minute, with a first-time shot from just outside the box but it sailed over.
Just three minutes later, Salah delivered the killer blow for the Nerazzurri, driving the ball through defenders after Van Dijk had headed towards his direction from a free-kick.
James Milner was brought on to ensure the Reds left the San Siro with their clean sheet intact and they did.
Van Dijk- back to his best
The Dutchman was back to his best tonight and completed three interceptions, won five out of seven aerial duels and made seven clearances.
He was a constant thorn in Dzeko and Martinez's sides, when they thought they had breached the Liverpool high-line, he was there. His recovery pace and strength was crucial.
The combination of Van Dijk and Konate with Fabinho in front of them was key to Liverpool restricting their opponents to zero shots-on-target.
Liverpool leave it late
The first half was end-to-end but the home side started to assert themselves in the second-half with an intensity that the Reds could not match.
However, Firmino and Salah dealt the decisive blows with less than a quarter of an hour remaining.
Liverpool have a knack for scoring late goals this season, 17 goals have been scored between the 76th and 90th minute.