The European champions surrendered a two-goal cushion with three minutes left to draw 2-2, heaping further misery on under-pressure manager Rafa Benitez. Thankfully for Benitez, Chelsea's leading rivals for the Champions League spots couldn't capitalize.
Fourth-place Tottenham only drew 1-1 thanks to Gareth Bale's solo goal that began in his own half, while Arsenal and Liverpool — the Premier League former heavyweights — missed a chance to close the gap on the top four by drawing 2-2 in an entertaining match at Emirates Stadium.
It meant fifth-place Everton was the big winner, beating West Bromwich Albion 2-1 to move one point behind Tottenham and pull three clear of Arsenal.
While a fierce race for the last two Champions League places intensifies behind them, United marches on toward a 20th title.
The leaders capitalized on second-place Manchester City's 0-0 draw at lowly Queens Park Rangers on Tuesday, but only after recovering from conceding a sloppy goal from a defensive mix-up and then withstanding a second-half onslaught by Southampton.
"My experience of this club, when you are going for championships, is that there are always games where you can say we were a bit lucky," United manager Alex Ferguson said. "This was one of those nights."
Rooney scored in the eighth and 27th minutes to make it nine goals in nine games for the England striker, who is finally starting to shine after seeing fellow striker Robin van Persie take most of the plaudits this season.
Those goals cancelled out Southampton's opener in the third minute, which arrived when Michael Carrick's weak back-pass wasn't cleared by goalkeeper David de Gea — allowing Jay Rodriguez to nip in and score.
Ferguson said Southampton's display was the best from a visiting side at Old Trafford this season.
"It's very important for my players to hear (that)," recently appointed Southampton manager Mauricio Pochettino said. "But we leave with no points. We did play well but I'm upset at not getting a draw at least. It doesn't console me."
Benitez was flabbergasted after seeing Chelsea throw away what seemed a watertight lead, when Adam Le Fondre halved the deficit and equalized in the fifth minute of injury time.
"The atmosphere was not good in the dressing room," Benitez said. "We did everything to win the game. For 85 minutes we were dominating everything.
"It is very difficult to take."
Juan Mata and Frank Lampard scored either side of halftime for Chelsea, which remains four points ahead of a Tottenham side rescued by the sublime skills of Bale in the 80th minute.
The Wales winger collected the ball inside his own half before embarking on a fast-paced dribble, which ended with him cutting inside and smashing a rising shot into the corner.
"It was nice to get a goal of that nature," Bale said, "and it was important to get back into the game."
Norwich had gone in front through Wes Hoolahan in the 32nd minute and will be happy with the point after losing embarrassingly to non-league side Luton in the FA Cup only five days earlier at Carrow Road.
Leighton Baines' first-half brace — one a powerful shot and the second a penalty — saw off West Brom at Goodison Park and boosted Everton's chances of qualifying for the Champions League.
Arsenal's draw with Liverpool did little to improve either side's hopes of climbing back into the top four, showing up both teams' deficiencies.
Shocking defending by the hosts let in Luis Suarez for the opener after five minutes and then Jordan Henderson in the 60th.
But Liverpool, without a win against a top-10 team all season, defended far too deeply thereafter and goals by Olivier Giroud and Theo Walcott earned Arsenal a point.
"We were outstanding going forward but nervous defensively," Arsenal manager Arsene Wenger said. "We showed quality and spirit to draw."
Fulham beat West Ham 3-1 with Dimitar Berbatov setting the home team on its way with the opening goal on his 32nd birthday.