Wesley Hoedt put the hosts — needing little help to do so — on the front foot with an own goal, before Joel Matip and Mohamed Salah each tallied in the first-half.
Mark Hughes was limited in his attacking options with Danny Ings unable to play against his parent club whilst Manolo Gabbiadini was absent through injury. Mohamed Elyounoussi also missed out through a knock.
It showed as Southampton threatened the Liverpool goal just once, which came in the 91st minute.
Southampton was fortunate Liverpool failed to add more, as Salah hit the back of the net for what would’ve been his 50th Premier League goal, only to be flagged offside.
Liverpool: Alisson, Alexander-Arnold, Matip, Van Dijk (Gomez 55), Robertson, Wijnaldum (Keita 70), Henderson, Shaqiri (Milner 46), Mane, Salah, Firmino.
Unused subs: Mignolet (GK), Fabinho Sturridge, Moreno.
Goals: Hoedt (OG 10), Matip (21), Salah (45+3).
Southampton: McCarthy, Bertrand, Hoedt, Vestergaard, Cedric, Hojbjerg, Lemina, Romeu (Armstrong 55), Targett (Bednarek 55), Redmond, Long (Austin 78).
Unused subs: Gunn (GK), Yoshida, Davis, Ward-Prowse.
Bookings: Romeu (34), Lemina (56).