In a dominant first-half performance, goals from Morgan Schneiderlin and a deflected Rickie Lambert free-kick put Mauricio Pochettino's side in the ascendancy.
Philippe Coutinho got Liverpool back into the game just before the interval, but Jay Rodriguez scored a deserved third goal with 10 minutes to go to lift Southampton seven points away from the relegation zone.
Southampton were ahead after just six minutes when Rodriguez nodded down Gaston Ramirez's cross into the path of Schneiderlin, who nonchalantly flicked the ball past Brad Jones.
Liverpool were sluggish for much of the first half and almost fell further behind on 10 minutes when Jones had to come off his line to deny Lambert after the striker had broken free.
Rodriguez had a well-struck shot from distance saved before the forward volleyed over on the turn from close range after Jones had parried Adam Lallana's attempt from a tight angle.
All Liverpool had to offer was an ambitious 35-yard shot from Daniel Sturridge which was easily gathered by Artur Boruc before Southampton extended their lead on 33 minutes.
The home side were awarded a free-kick 30 yards from goal and Lambert's shot took a wicked deflection off the jumping Sturridge before creeping inside the post.
Jones then saved again from Rodriguez before Coutinho had the chance to pull a goal back five minutes before half-time after bursting clear, only to shoot straight at Boruc.
Southampton were playing some sublime football on the South Coast and another slick move created an opening for Lallana, but he shot just wide.
Liverpool gave themselves hope for the second half by scoring in first-half stoppage-time when Coutinho fired home the loose ball after Sturridge's shot had been blocked.
Chances proved to be more scarce after half-time, with Sturridge scuffing wide before Luis Suarez and Steven Gerrard both drew comfortable saves out of Boruc.
Jones was out again to deny Lallana on 77 minutes, but three minutes later he was beaten for a third time when Rodriguez was allowed to run virtually unchallenged from the halfway line and he tucked away the rebound after his initial shot had been pushed out by the Liverpool keeper.