The game, which took place at the Anfield stadium, ended 4-0 in favor of the Merseysides.
For Liverpool, Diogo Jota scored a double in the first half (in the second and 32nd minutes).
Thiago Alcantara (in the 37th minute) and Virgil van Dijk (in the 52nd minute) also distinguished themselves.
Liverpool, with 28 points, are in second place in the standings.
"Southampton" with 14 points - on the 14th line.
The leader in the Premier League is Chelsea (29), which in the 13th round match on 28 November will host Manchester United (17).
Earlier it was reported that Arsenal scored two unanswered goals to Newcastle in the Premier League match.