It was another fine comeback in Klopp's 11th game in charge as Southampton took the lead before the reds bounced back hitting six goals against the men on the south coast.
The reds victory was met with jubilation by Liverpool's fans at the stadium and elsewhere.
Liverpool now go on to meet Stoke City in the Semi Final of the League Cup - a record 16th appearance for LFC in the semi-finals of that competition.
Here you can watch extended highlights of last night's game.