After a goalless opening 45 minutes, the Blues took an early second-half when Leroy Sane raced clear and found the bottom corner with a near finish.
However, the Reds introduced Salah just after the hour – and he took less than 70 seconds to make his mark when he headed in Rafa Camacho’s cross from six yards out.
And Mane secured the win for Liverpool deep into stoppage-time when he converted a penalty after Dominic Solanke had been barged over inside the area.
Ahead of the game, it was confirmed Georginio Wijnaldum would make first appearance of the summer as he started in midfield, while Salah and Mane were joined by Marko Grujic on the bench.