Two first-half goals from Roberto Firmino and Mohamed Salah sealed the win for Liverpool.
Salah have now scored 29 goals in all competitions for Liverpool this season, 22 in the league, while Firmino has 20 also in all competitions.
The win lifted Jurgen Klopp’s men to third on 54 points in the league table.
Firmino tucked the ball home early on to put his side 1-0 up after being teed up by Mohamed Salah who capitalised on a defensive mistake.
In the 18th minute, Southampton went close through Pierre-Emile Hojbjerg who failed to beat Loris Karius one on one.
Karius was called into action again in the 29th minute, denying both Guido Carrillo and James Ward-Prowse.
Southampton were made to pay for their missed chances as Salah doubled Liverpool’s lead, sweeping home off a Firmino assist.
In the 57th minute, Ward-Prowse delivered a dangerous cross which Wesley Hoedt failed to divert goal ward.
Firmino almost extended Liverpool’s lead on 71 minutes only for Alex McCarthy to make a brilliant save before Salah failed to convert the rebound.
On 76 minutes, Sadio Mane was the next to miss a good chance as he blasted his effort just wide of the left upright after initial good play from Goergino Wijnaldum.
With five minutes left Adam Lallana saw his attempt drift just wide off target.