Roberto Firmino and Mohamed Salah combined for both goals at the beginning and end of the first half as Liverpool returned to winning ways in the top flight, handing Jurgen Klopp his 50th Premier League victory as manager.
Southampton were unable to fight back in the second half as they end the weekend in the bottom three and a point from safety, while Liverpool climb back up to third after momentarily dropping a place following Tottenham Hotspur's win over Arsenal on Saturday.
The Reds have now lost just one of their last 18 Premier League games, whereas Southampton equal an unwanted club record of seven successive home games without a Premier League victory.
Southampton went into the match having already endured a disappointing day before kickoff, with wins elsewhere for Huddersfield Town and Newcastle United seeing them drop into the relegation zone prior to their own game getting underway.
Things only got worse in the opening stages of the match too as Liverpool broke the deadlock after just six minutes, with Salah pouncing on a mistake from Wesley Hoedt before teeing up Firmino, who buried his confident first-time finish into the bottom corner.
It was a sloppy start from the home side, and Liverpool almost doubled their advantage shortly afterwards when Alex Oxlade-Chamberlain - one of five former Southampton players in the visitors' matchday squad, including January arrival Virgil van Dijk - saw his deflected drive kept out by Alex McCarthy.
Southampton did soon begin to settle into the game, though, and Jack Stephens had their first shot on goal when he dragged a long-range effort wide of the target while looking to score for a fourth successive game.
The hosts' first big chance arrived after 18 minutes when Oriol Romeu's perfectly-weighted pass picked out Pierre-Emile Hojbjerg inside the box, but Loris Karius was quick off his line to thwart the Southampton midfielder.
Sadio Mane dragged a long-range effort wide of the target eight minutes later, but it was Southampton who were on top despite the early setback and Mauricio Pellegrino's side looked increasingly like getting an equalising goal.
Southampton continued to knock on the door, though, and Ward-Prowse was on the other end of two dangerous crosses to the back post, but saw both of his headers saved.
It was Liverpool who added the game's second goal against the run of play, though, adding a late first-half strike to their early one as Salah and Firmino once again combined to devastating effect.
Firmino collected the ball from Salah before producing an exquisite flick back into the Egyptian's path, and Salah made no mistake with his finish into the bottom corner for his 29th goal of the season.
The strike also saw Salah draw level with Liverpool legend Robbie Fowler's record of most left-footed goals in a Premier League campaign, with 19 of his 22 top-flight goals now having come with his favoured foot.
The two-goal lead was harsh on Southampton going into half time, but it almost got worse in the opening stages of the second half when Mane's acrobatic effort was blocked and fell at the feet of Salah, although this time the prolific winger scooped his finish over the crossbar.
Liverpool were able to remain in control of the contest after their bright opening in the second half, though, dominating possession and preventing the home side from building any momentum in their search for a route back into the game.
Southampton did have one threat which saw Hoedt dart across the near post to meet a devilish delivery from Ward-Prowse, but he got too much on his attempted flick to put it past the near post.
It was Liverpool who looked most likely to add to the scoring throughout the second half, and Firmino came close to doubling his own tally when his low strike was well saved by McCarthy before Salah could only find the side-netting with a follow-up effort.
Mane then skewed a shot wide of the near post while off balance as he looked to join his fellow attackers on the scoresheet, before Adam Lallana also came close shortly after being introduced as a sub.
The Reds ultimately settled for a two-goal victory and a rare away clean sheet too as they capitalised on Manchester United's shock defeat earlier in the day to move to within two points of their bitter rivals in second.
Klopp's tally of 50 Premier League wins from 95 games matches that of predecessor Brendan Rodgers, whereas his Southampton counterpart Pellegrino is sure to face more questions over his future after seeing his side booed off by sections of the home crowd.
SOUTHAMPTON (4-2-3-1): McCarthy; Cedric, Stephens, Hoedt, Bertrand; Romeu (Davis, 80'), Lemina (Boufal, 57'), Ward-Prowse (Long, 71'), Hojbjerg, Tadic; Carrillo
LIVERPOOL (4-3-3): Karius; Alexander-Arnold, Matip, Van Dijk, Robertson; Oxlade-Chamberlain (Milner, 60'), Can, Wijnaldum; Salah (Lovren, 89'), Firmino (Lallana, 79'), Mane