The meeting at Anfield ended 2-0 in favor of the home team.
The victory for Liverpool was brought by goals from Sadio Mane and Thiago Alcantara, who distinguished themselves in the 31st and 90th minutes.
Liverpool scored 57 points and moved up to sixth in the Premier League standings.
Southampton with 37 points - 16th.
In another match of the game of the day, Crystal Palace beat Sheffield United away (2: 0).
Earlier it was reported that Arsenal did not make it to the top 4 of the Premier League for the fifth year in a row.