Olivier Giroud gave Frank Lampard’s side a deserved first-half lead on Wednesday, but the introduction of Roberto Firmino as a half-time substitute changed the game for the Reds.
Firmino quickly set up Mane for the equaliser and, in the first period of extra time, the Senegal star smashed home from his team-mate’s pass again before Jorginho equalised from the penalty spot.
But it was the European champions who triumphed in the shoot-out, Alisson’s deputy Adrian denying Abraham with his right leg to secure victory for Jurgen Klopp’s side.