Dominic Solanke opened the scoring in the 15th minute before Mane, back after knee surgery, set up Georginio Wijnaldum for Liverpool's second just past the half-hour.
Salah continued Liverpool's impressive pre-season form when he completed the scoring in the 60th minute, finishing off a lofted pass from Philippe Coutinho.
Perhaps with recent speculation over his future in mind, Jurgen Klopp handed the captain's armband to Coutinho, with the Brazil international playing on the left of the front three in the first half. Sadio Mane also started as he made his first appearance since suffering a knee injury in April.
The lively Mitchell Weiser dragged an early shot wide for Hertha, who finished sixth in the Bundesliga last season, before Vladimir Darida shot at Simon Mignolet.
But Liverpool broke the deadlock after 15 minutes when Solanke looped a header over Rune Jarstein from Adam Lallana's chipped cross.
The Reds looked in control of proceedings and Mane volleyed over from inside the box. Hertha's best moments came down the right, with Ondrej Duda seeing a shot deflected wide after Weiser beat Ragnar Klavan to the ball.
Wijnaldum made it 2-0 when he fired in from the edge of the box after Solanke pressed Fabian Lustenberger in the corner and forced a mistake.
Salah, Roberto Firmino and Daniel Sturridge were introduced at half-time along with Andrew Robertson, making his first appearance after his move from Hull.
Liverpool dominated the second half and Robertson shot at the keeper before Firmino saw an effort tipped over.
Robertson then provided an overlapping run down the left and put in a well-directed cross that Salah could not quite turn in at the back post.
Salah did net in the 62nd minute, lifting the ball over the goalkeeper after an inch-perfect pass over the top from inside his own half by Coutinho.
Firmino and Sturridge went close to extending the lead as Liverpool saw out a comfortable win.
Related links
Walcott at the double for Arsenal
Chelsea beaten by Inter
A round-up of the other pre-season action
