Blades goalkeeper Paddy Kenny proved the villain as his first-half blunder gifted Saints striker Jhon Viafara with the winner just after the half-hour mark.
Kenny spilled Andrew Surman's free-kick and Colombian Viafara pounced to stab home the loose ball.
Keith Gillespie had earlier fired United in front only for the Saints to equalise with their first serious attack in the 19th minute through Grzegorz Rasiak.
Under Bryan Robson, who succeeded Neil Warnock as boss in May, United have won only two of their eight league matches and what was supposed to be a promotion charge has turned into an early-season scramble to steer clear of the drop zone following their cruel exit from the top flight last season.
Robson recalled skipper Chris Morgan to his starting line-up, with recent loan signing Gary Cahill, Keith Gillespie, Jon Stead and James Beattie all returning after sitting out the midweek Carling Cup win over Morecambe.
Lee Hendrie made his first league start since the opening day of the season.
Southampton manager George Burley recalled four players to his starting XI. Rasiak, Alexander Ostlund, Phil Ifil and Nathan Dyer were all hoping to help end the Saints' three-match run without a win.
Stead wasted little time in making an early impression when his first-minute header from Gillespie's free-kick was comfortably saved by Kelvin Davis.
But before the visitors had mustered any worthwhile attacks, the Blades took the lead.
Gillespie latched on to Kenny's clearance and cut in from the right wing before burying a low shot inside the near post in the 12th minute.
Beattie flashed a volley wide soon afterwards, but then Southampton equalised with their first shot on goal.
Dyer picked out an unmarked Rasiak in the penalty area from the left and the Poland international coolly steered a left-footed shot into the bottom corner.
Bradley Wright-Phillips kept Kenny on his toes with a 25-yard shot, but the Blades goalkeeper was less impressive as Southampton snatched a 31st-minute lead.
Kenny could only flap at Surman's free-kick to divert the ball into the path of Viafara and the Colombian pounced to toe-poke his second goal of the season.
The Blades monopolised possession early in the second period without creating a true opening, until Gary Naysmith's wayward cross forced Davis into a brilliant save.
Naysmith and Hendrie made way for Chris Armstrong and Michael Tonge in the 63rd minute, while Marek Saganowski replaced the injured Wright-Phillips for the visitors.
Beattie went close to hauling United level, but his header from Geary's cross cleared the crossbar before boss Robson threw on another striker, Luton Shelton, for Gillespie.
But Dyer's drive and a Rasiak header that forced a timely clearance from Geary served warning to the home side that Southampton still harboured attacking intentions and it was Burley's side who finished the stronger.
Shelton was forced to block Viafara's stinging free-kick in the closing stages and the Blades failed to mount a late fightback as Southampton bounced back from last week's home defeat to Barnsley.