Ralph Hasenhuttl's side registered a superb victory over Tottenham before the international break and picked up where they left off as Pierre-Emile Hojbjerg's solitary goal handed them a deserved win over their lacklustre hosts.
Brighton offered little in the way of an attacking threat but came close to securing an unlikely point 20 minutes from time when Martin Montoya thundered an effort against the post.
Chris Hughton's men had won their previous two games and knew a third on the spin would have given them a glorious chance of securing their top-flight status for another season. As it is, they remain on 33 points, alongside Southampton, and still have work to do in their remaining eight games.
Nathan Redmond carved out the first sight of goal midway through the first-half, cutting in from the left and firing straight at Mat Ryan.
Brighton struggled to break down the Saints with Yves Bissouma's low shot from 25 yards, which rolled past Angus Gunn's right-hand post, all they had to show for their first-half efforts.
Redmond again came close shortly before the interval, fizzing wide from an acute angle after being played in by Danny Ings.
Former Norwich City winger Redmond was the architect of his side's opener eight minutes after the interval, though. He powered into Brighton's penalty area after the hosts had given possession away inside their own half and played in Hojbjerg, who clipped a wonderful finish past Ryan with the outside of his right foot.
That goal belatedly woke Brighton from their slumber and Montoya came agonisingly close to restoring parity, his left-foot strike from the edge of area crashing back off Gunn's right-hand post.
Brighton huffed and puffed in the closing stages but the Saints never truly looked like relinquishing their lead as they continue their march towards Premier League survival.
What does it mean? Saints finding form at the right time
Three wins out of four has given Southampton a glorious opportunity to preserve their Premier League status – something that did not look likely when Mark Hughes was sacked in December. Not only is Hasenhuttl delivering results, but he has got the Saints playing some eye-catching football, as evidenced by the incisive move for Hojbjerg's goal. Brighton, meanwhile, know they have enough games left to pick up the requisite points but will certainly see this as a missed opportunity.
Redmond too hot to handle
Playing alongside Ings up front, Redmond was comfortably Southampton's brightest spark. He twice came close in the first half and then showed superb composure to play in Hojbjerg for the game's decisive moment.
Murray needs to rediscover home comforts
After scoring in six of his first seven league appearances at home this season, Murray has now failed to score in his last eight games at the Amex Stadium. He rarely looked like getting on the scoresheet against a Saints side who kept him at bay with the minimum of fuss.