The visitors made a lively start, threatening within the first two minutes after Nathaniel Clyne exchanged passes on the edge of the box before hitting a shot across goal, but his effort flew narrowly wide of the post.
Despite the burst of early action, the game's tempo slowed down as both sides played a patient game in a bid to suss out their opponents.
After just twenty minutes, Southampton suffered a setback when Toby Alderweireld was forced off with a leg problem he suffered after attempting to clear a ball.
United were failing to click in the final third for most of the first half, but stepped it up a gear towards the latter stages when Angel di Maria and Robin van Persie mustered two dangerous chances on goal.
Southampton proved sturdy in defence, closing down their opponents time after time, and went one better when they took the lead in the 68th minute.
United set about trying to find an equaliser and probed forward at every opportunity, coming close in the 77th minute when Daley Blind's cross from the left almost caught Fraser Forster out, before Juan Mata shot wide moments later.
Southampton, however, were able to see the game out and secure three well-earned points to leapfrog the Red Devils into third place.