Brendan Rodgers' men climbed to second in the Premier League after overcoming a lively Saints outfit thanks largely to the attacking exploits of their Uruguayan striker.
After Arsenal slipped up at Stoke City earlier in the day, pressure was on Liverpool as the club sought to arrest a run of three straight away defeats to Southampton and avenge a home reverse to the south-coast club from earlier in the season.
However, a goal in each half from Luis Suarez and Raheem Sterling and a late penalty from Steven Gerrard ended the poor run of form against the home side and kept the team within four points of Chelsea - having played two games more than fourth-placed Manchester City.
Making his 100th Premier League appearance, Suarez opened the scoring early on - calmly slotting home from inside the penalty area after an attempted clearance ricocheted into his path off Jose Fonte.
His 62nd goal in the top flight ended a run of nearly seven hours without finding the net and he turned provider for Liverpool's second shortly before the hour mark.
The striker's pull back from the right was met by substitute Sterling who added a second, before Steven Gerrard stroked home a stoppage-time penalty to add an emphatic touch to the score line and ensure Liverpool of a first win at Southampton since 2003.
Southampton's England quartet of Luke Shaw, Jay Rodriguez, Rickie Lambert and Adam Lallana all started the game, with national manager Roy Hodgson watching on.
However Uruguay international Suarez, who will face England in Brazil, almost gave the visiting side the lead after just six minutes, though he was unable to apply a finishing touch to Daniel Sturridge's cross due to Fonte's well-timed intervention.
Suarez was on hand to take advantage of slack Southampton defending 10 minutes later however, sliding home a loose ball from inside the area after the Saints failed to clear.
Despite falling behind, Southampton continued to keep possession and Lambert could have threatened Simon Mignolet's goal after 25 minutes but he could only angle his snap shot over the crossbar.
Rodriguez's knockdown then found Lallana inside the area but the midfielder rolled his effort onto Mignolet's right-hand post shortly after the half-four mark before failing to direct Shaw's cutback on target.
Mignolet then produced an impressive stop two minutes before the break, clawing away Rodriguez's sidefooted effort as the home side was frustrated in its attempts to level.
Southampton continued the momentum into the second half but was unable to breach Liverpool's defense while Brendan Rodgers opted to introduce Sterling in an attempt to offer more of a forward threat.
It proved an astute decision as the winger slid home Suarez's cross to double Liverpool's advantage two minutes before the hour on his 50th Premier League appearance.
Gerrard capped off an important outing for his side with a late penalty, won by Suarez, as Liverpool racked up a fourth straight win in the top flight to reinforce the club's credentials as a title hopeful.