The Red Devils move seven points clear at the top of the Premier League while a first defeat in six games leaves the Saints only three points above the relegation zone
Jay Rodriguez capitalised on a mistake from Michael Carrick to give the Saints a shock early lead but a double from Wayne Rooney had the hosts in front by half-time.
The Saints improved in the second half, with Rickie Lambert testing David de Gea on a couple of occasions, but the league leaders were worth their win despite a nervy end.
Sir Alex Ferguson reinstated Robin van Persie back into his attacking-looking starting line-up, with Danny Welbeck, Shinji Kagawa and Rooney supporting the Dutchman while Nemanja Vidic returned in defence.
Mauricio Pochettino made two changes from the draw against Everton, Danny Fox and Rodriguez replacing Luke Shaw and Guly do Prado.
The hosts got off to an awful start when Carrick's backpass put De Gea in all sorts of trouble in the third minute. Rodriguez pounced, taking a touch to beat the United keeper before passing it into an open net.
The Saints' lead didn't last long, however, as Rooney fired the hosts level five minutes later when he timed his run on to Kagawa's lobbed pass and stroked the ball easily past Artur Boruc.
The Japan international was involved again moments later, getting down the left flank and cutting inside before striking a shot on to the near post.
Southampton were pegged back in their own half from then on and could only hold off the Red Devils' attacking onslaught until the 27th minute.
Van Persie drifted a deep free kick towards Boruc's back post, where Evra was on hand to head the ball back across the box for Rooney to turn into the net from a yard out.
The Saints started the second period brightly, with Lambert forcing De Gea to make his first save with a tame volley.
Pochettino's men continued to apply pressure and could have gone ahead on the hour mark when Lambert hit the target with a fierce free kick. De Gea spilled the initial effort but cleared before Adam Lallana could pounce on the loose ball.
United weathered the Saints' storm and then created some chances of their own with Rooney and Kagawa combining to drive Sir Alex Ferguson's side forward.
Van Persie thought that he had added his name to the scoresheet in the 75th minute when he headed past Boruc at the second time of asking but the Dutchman had his celebrations cut short by a harsh offside decision.
Lambert then came close to grabbing the equaliser with another free kick; the Saints striker curled an effort perfectly over the wall only to see De Gea make an outstanding low save.
Rooney then wasted a chance to seal his hat-trick when he was slid through by Van Persie but the England forward took a bad touch, allowing Boruc to smother.