Champions Manchester City's 0-0 draw at bottom club Queens Park Rangers 24 hours earlier paved the way for United to widen the gap but Jay Rodriguez silenced the home crowd after three minutes before Rooney's double restored order before half-time.
Apart from Everton, the clubs battling for top-four finishes and Champions League qualification suffered frustration, none more so than third-placed Chelsea who threw away a two-goal lead to draw 2-2 at struggling Reading for whom substitute Adam Le Fondre struck twice in the closing stages.
Chelsea remain four points clear of Tottenham Hotspur who needed a superb Gareth Bale equaliser in a 1-1 draw at Norwich City while sixth-placed Arsenal drew 2-2 at home to Liverpool having trailed 2-0 with half an hour remaining.
Luis Suarez gave Liverpool an early lead and Jordan Henderson made it 2-0 on the hour after some terrible Arsenal defending but Olivier Giroud and Theo Walcott earned the Gunners a deserved point from an entertaining clash.
Fifth-placed Everton cashed in on the dropped points of those around them in the table with a 2-1 home victory over West Bromwich Albion to move one point behind Tottenham, three clear of Arsenal and six ahead of Liverpool.
In a London derby alongside the River Thames, Fulham beat West Ham United 3-1.
Eight of United's previous 18 league wins this season had come from losing positions and they needed to dig in again after Rodriquez punished a poor Michael Carrick back pass to give Southampton a dream start at a ground where they had lost on 15 of their last 16 visits.
United were stunned into life though and were level five minutes later when Shinji Kagawa's defence-splitting pass was finished stylishly by Rooney.
The England striker then tapped in from close range after 27 minutes but the expected United domination failed to materialise as Southampton made it an awkward night for the leaders.
"Winning is the name of the game at this stage of the season," United manager Sir Alex Ferguson said.
"For the first 30 minutes I thought we were fantastic, we played really well. But in the second half Southampton have been the best team to play here this season.
"We were fortunate to win the game."
Southampton might have earned a draw late on when Rickie Lambert's free-kick forced a flying save from David de Gea.
Chelsea took the lead on the stroke of half-time through Juan Mata and Frank Lampard's thumping header should have secured the points for Rafa Benitez's team but they suffered a late ambush.
Le Fondre, who came on after 66 minutes, gave Reading hope when he drilled in a shot after 87 minutes and deep into stoppage he calmly side-footed his side's equaliser to move his side out of the bottom three.
He has now scored six goals after coming on as substitute this season, more than any other player in the top flight.
Benitez was not impressed with his side's collapse.
"The atmosphere was not good in the dressing room," he said. "It's very difficult to take."
Rumblings of discontent were growing around Emirates Stadium as Arsenal's Swiss-cheese defence allowed Liverpool into a two-goal lead although their response was impressive.
Suarez benefited from a catalogue of stumbles, slips and poor clearances to bag his 17th league goal of the season early on and Henderson managed to get through several attempted tackles to put Liverpool two up after 60 minutes.
Giroud then headed Arsenal
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