The visitors were already trailing to Mohamed Salah’s sweeping finish when Mane turned a couple of Cardiff defenders before turning and finishing past Neil Etheridge.
Virgil van Dijk nodded against a post while Adam Lallana was denied by Sean Morrison’s headed clearance off the line as the Reds dominated for long spells.
Cardiff pulled a goal back with their first shot on target 13 minutes from time, Callum Paterson steering past Alisson.
But substitute Xherdan Shaqiri restored the two-goal cushion with his first goal for the club and Mane chipped Etheridge to seal the points.
Jurgen Klopp’s side will stay on top until at least Monday, when City take on fifth-placed Tottenham at Wembley.
