Going into the clash, the Reds’ drive towards the title meant they needed the win more than their London visitors, but a Manchester City 3-1 victory over Crystal Palace at Selhurst Park - that pushed the hosts to the second spot - meant they headed into the match the more pressured side.
After a cagey first half that saw the duo unable to convert half chances; one which they took turns to create, they sparked to live within two second-half minutes, with Salah's piledriver sealing his former employers’ defeat.
Mane header at the back post, off a perfect Jordan Henderson cross, put Jurgen Klopp's men in front in the 51st minute before Salah rifled in a long-range effort to the top left corner to double their lead two minutes later.
Chelsea, through Eden Hazard, had two chances to half their deficit but the woodwork and Alisson respectively stood in their way.
Mane, who was the Premier League Player of the Month for March, continues his rich vein of form while Salah would be glad
Guinea midfielder Naby Keita continued his impressive form in the Reds’ midfield and was excused after the hour mark.
Liverpool are now two points better than second-placed City  who have a game in hand and will hope to keep up with the momentum.