A stunning first-half finish from Danny Ings was sufficient to secure the points for the home side.
But who were the standout performers in the contest?
✔️ GOOD PERFORMANCE
James Ward-Prowse: 7.5
England international Ward-Prowse was critical for Southampton at both ends of the field. His clever free kick provided the assist for the only goal of the game, while he showed impressive creativity when given a chance.
He was also effective defensively, though. He made an impressive 12 recoveries in the heart of the field for the home side.
Danny Ings: 7.0
James Ward-Prowse delivered a free kick into the left channel. Ings lofted the bouncing ball spectacularly over Alisson from a testing angle.
He would have few sights of goal before going off with 13 minutes remaining, but he was still the match winner.
❌ BAD PERFORMANCE
Liverpool have come to expect much of young right-back Alexander-Arnold, but his less-than-spectacular season continued at St Mary's.
It was an encounter in which the Reds struggled to make the most of their assets from deep, yet defensively Alexander-Arnold performed wretchedly.
He won only one of his eight duels and was unsuccessful in the only aerial duel he attempted.
⭐ STAR MAN
Jack Stephens: 8.3
Southampton came under significant pressure over the course of this match, ceding around two-thirds of possession to their opponents.
Fraser Forster's goal, though, rarely looked under serious threat, with much of that owing to a robust performance from the back four.
There was not a failure in the Saints rearguard, but it was the former England Under-21 man who was the outstanding figure.
He won the only tackle he attempted, the only aerial duel he attempted and won three of his six duels. On top of that, he made a match-high five interceptions and made several important blocks.