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Liverpool's prize for hitting Southampton for six is a Capital One Cup semi-final meeting with Stoke.
Jurgen Klopp's Reds destroyed sorry Saints 6-1 at St Mary's in their quarter-final meeting on Wednesday, with a Daniel Sturridge double, a Divock Origi hat-trick and a superb Jordon Ibe effort finishing the hosts off.
It means Liverpool, who will make a record 16th appearance in the last four, face the Potters, who have not reached this stage since winning the competition in 1972.
Liverpool's city rivals Everton, who have never won the League Cup, face 2014 winners Manchester City in the other semi-final.