Match ends, Southampton 0, Liverpool 2.
Southampton manager Mauricio Pellegrino claimed the "biggest defeat" his side suffered in their loss to Liverpool was "the character we showed in the second half".
Liverpool moved to within two points of second-placed Manchester United after goals from Roberto Firmino and Mohamed Salah secured a comfortable victory.
Brazil forward Firmino gave Liverpool an early lead with his 20th goal of the season when he finished off a counter attack after being teed up by Salah.
Southampton then twice brought saves out of Reds goalkeeper Loris Karius, before Liverpool added a second through Salah after he exchanged passes with Firmino.
It was the Egypt international's 29th goal of the season for the club from 36 appearances.
Liverpool looked the more likely to score again after half-time as Southampton rarely threatened.
"The second half was really bad. The people see our reaction on the pitch and the players feel the reaction," Pellegrino said.
"The anxiety in my players was really high. We understand the emotions of the fans but we have to keep going."
The win ensured Liverpool took advantage of Manchester United's 1-0 defeat by Newcastle earlier on Sunday and leapfrogged Tottenham back into third place.
Southampton drop into the relegation zone, a point behind Huddersfield who beat Bournemouth 4-1, with further scrutiny of Pellegrino's position likely.
Van Dijk keeps his cool
Liverpool defender Virgil van Dijk was expected to get a hostile reaction from the Southampton fans on his first return to St Mary's since his move to Anfield, and there were plenty of boos for the Dutchman.
Indeed, Reds manager Jurgen Klopp revealed in the build-up to the match he would speak to Van Dijk about the need to maintain his composure in light of the ill-feeling towards him.
The 26-year-old, whose protracted move to the Reds for £75m from Southampton was eventually completed in January after the transfer saga of last summer, more than kept his cool at the heart of Liverpool's defence.
His performance was one with which the Southampton fans would have been familiar - towering headers, key interceptions and brave blocks while marshalling the backline.
It was this kind of faultless defensive display Liverpool fans had yearned for before his arrival, and the kind Southampton now so desperately miss.
Southampton need more from Carrillo
Southampton's victory over West Brom in their previous match ended a run of 12 league matches without a win, but this defeat will have damaged their confidence.
A sluggish start and defensive mistakes - with Wesley Hoedt the most culpable - allowed Liverpool to take the lead with a quicksilver counter-attack finished off by Firmino.
There was little the hosts could do about Liverpool's second as Firmino's brilliant backheel set up Salah.
But the worry for Saints fans will be how toothless they were in attack at home, and particularly the lack of threat posed by Guido Carrillo.
Pellegrino made striker Carrillo their club record £19m signing from Monaco in January, but the Argentine has yet to find the net.
Southampton need Carrillo to show more from here until the end of the season if they are to avoid the drop.
Karius builds case to start in Porto
Liverpool manager Klopp has rotated goalkeepers Karius and Simon Mignolet according to competition this season.
Whichever man has not been first choice in the Premier League has instead started in the Champions League.
Klopp stated last month that Karius would be his first choice for league matches, but under his policy to date Mignolet would return in goal for the first leg of their Champions League last-16 tie away to Porto.
However, the impressive display by Karius at St Mary's will surely prompt Klopp to rethink his approach, particularly as the European competition represents Liverpool's last hope of a trophy this season.
With Liverpool 1-0 up against the Saints the German made two fine saves - narrowing the angle to block a Pierre-Emile Hojbjerg shot and tipping a James Ward-Prowse header over the crossbar - while his quick distribution played a part in Firmino's opening goal.
Will Klopp now risk bringing back Mignolet for such an pivotal game on Wednesday? If he does bank on Karius in Portugal, it could well signal the end of Mignolet's Anfield career given the Belgian's desire to play regularly.
'We don't have normal weekends anymore'
Liverpool manager Jurgen Klopp: "It was not a brilliant performance, not everything worked quite well, the wind was quite strange. It was difficult circumstances and we did the job. That is very important.
"We scored early, got the second goal in the right moment and then controlled the game.
"We don't have normal weekends anymore. We want to finish the season top four and we need the points. I don't think nine points from Arsenal is enough to have rest but it is nine points. There is a lot to go for and we will try to carry on like today."
Liverpool winger Mohamed Salah: "I said in beginning, I always try to help the team. When you score of course you help the team.
"So I'm not surprised, but we need to forget about the past and keep looking forward. We have more league games and the Champions League."
Man of the match - Roberto Firmino (Liverpool)
Salah puts left foot first - the best stats
- Jurgen Klopp has won 50 of his 95 Premier League games in charge (D28 L17) - the ninth fastest manager to reach 50 wins.
- Southampton have won just once in their past 14 Premier League games (D7 L6), and kept only one clean sheet in the process.
- Liverpool have already scored more Premier League away goals in this campaign (34) than they managed in the entirety of 2016-17 (33).
- Mohamed Salah has been directly involved in 29 Premier League goals this season (22 goals, 7 assists), the most by a Liverpool player in their debut season.
- Salah has scored 19 left-footed goals in the Premier League this term - the joint-most by a player in a single season, alongside Robbie Fowler for Liverpool in 1994-95.
- Only twice in the past 16 seasons have Liverpool seen two players score 20 times in a campaign in all competitions. Salah has 28 and Roberto Firmino 20.
Liverpool travel to Porto for the first leg of the Champions League last-16 tie at the Estadio do Dragao on Wednesday (19:45 GMT). Southampton are in FA Cup action on Saturday (15:00 GMT) when they face West Brom in a fifth-round tie at The Hawthorns.
- 2Cédric Soares
- 14RomeuBooked at 62minsSubstituted forDavisat 80'minutes
- 18LeminaSubstituted forBoufalat 57'minutes
- 16Ward-ProwseSubstituted forLongat 71'minutes
- 32MatipBooked at 37mins
- 4van Dijk
- 21Oxlade-ChamberlainSubstituted forMilnerat 60'minutes
- 23CanBooked at 47mins
- 11SalahSubstituted forLovrenat 89'minutes
- 9FirminoSubstituted forLallanaat 79'minutes
- Martin Atkinson
- Shots on Target
Second Half ends, Southampton 0, Liverpool 2.
Foul by Emre Can (Liverpool).
Shane Long (Southampton) wins a free kick in the defensive half.
Substitution, Liverpool. Dejan Lovren replaces Mohamed Salah.
Attempt missed. Adam Lallana (Liverpool) left footed shot from the centre of the box is close, but misses to the left. Assisted by Mohamed Salah with a through ball.
Foul by Wesley Hoedt (Southampton).
Adam Lallana (Liverpool) wins a free kick in the attacking half.
Substitution, Southampton. Steven Davis replaces Oriol Romeu.
Cédric Soares (Southampton) wins a free kick in the defensive half.
Foul by Sadio Mané (Liverpool).
Substitution, Liverpool. Adam Lallana replaces Roberto Firmino.
Attempt blocked. Roberto Firmino (Liverpool) right footed shot from outside the box is blocked.
Attempt missed. Sadio Mané (Liverpool) left footed shot from the centre of the box is close, but misses to the left. Assisted by Roberto Firmino.
Attempt blocked. Andrew Robertson (Liverpool) left footed shot from the left side of the box is blocked.
Attempt blocked. Sadio Mané (Liverpool) right footed shot from the centre of the box is blocked. Assisted by Virgil van Dijk.
Substitution, Southampton. Shane Long replaces James Ward-Prowse.
Attempt missed. Mohamed Salah (Liverpool) left footed shot from the centre of the box is close, but misses to the right.
Attempt saved. Roberto Firmino (Liverpool) right footed shot from the centre of the box is saved in the bottom left corner. Assisted by Sadio Mané.
Offside, Southampton. Guido Carrillo tries a through ball, but Dusan Tadic is caught offside.