The hosts took the lead through Shane Long, with the forward hitting from close range after nine minutes.
Jurgen Klopp's men responded just under 30 minutes later as Naby Keita headed home his first goal of the season at the far post.
Liverpool faced an anxious wait for the second and it was eventually Mohamed Salah who stepped up to deliver, scoring a sublime solo goal in the 80th minute.
Jordan Henderson wrapped up proceedings with an easy tap-in six minutes later to make sure of the win.
So how did the two teams fare? See the gallery below for our player ratings.
Southampton vs Liverpool: Player ratings
Show all 22
Join our commenting forum
Join thought-provoking conversations, follow other Independent readers and see their replies
Join our commenting forum
Join thought-provoking conversations, follow other Independent readers and see their replies