Liverpool had taken the lead through Robert Firmino's strike, before Mohamed Salah smashed home a goal before half time.
Mane had won a penalty which Salah dispatched, and had just missed his own chnace to convert from the spot before this goal.
The home team continued to press high up the pitch despite their commanding position, with the ball ending up with Danny Sturridge after recovering it.
The striker slid the ball through to Mane, who was unmarked, and the Senegalese stabbed the ball under the Red Star goalkeeper to add a fourth goal for the home side.