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.
This was not as straightforward as the result suggests, with Liverpool requiring two late goals to finally see off Cardiff – who scored from their first shot on target to make it 2-1 in the 77th minute.
Yet the hosts’ quality shone through and they will travel for a huge test at Arsenal next Saturday as leaders unless Pep Guardiola’s City beat Spurs.
The positives keep on coming for Klopp.
Mane produced two delicious finishes, while Salah supplied two assists as well as providing the early breakthrough.
Cardiff looked like they would be buried as the Reds dominated possession – yet it required a wonderful finish from Mane to double the lead midway through the second half.
The one big disappointment as far as Liverpool were concerned was Paterson’s goal, which denied them a 10th successive Premier League clean sheet at Anfield.
However, it proved only a blip as Shaqiri and Mane went on to seal the points following two late Salah assists.
Jurgen Klopp’s side will stay top of the table until at least Monday, when City take on fifth-placed Tottenham at Wembley (20:00 GMT kick-off).