Southampton took a shock third minute lead when Michael Carrick's poor back-pass saw Jay Rodriguez dispossess United goalkeeper David de Gea before he rolled the ball into the net.
However, United were only behind for five minutes with Rooney equalising after he was played in by Shinji Kagawa.
The England striker made it 2-1 from a yard out in the 27th minute after a Robin van Persie free-kick was headed back across goal by Patrice Evra.
"[Winning] is the name of the game at this stage of the season," United manager Alex Ferguson told the BBC.
"In the second half Southampton were the best team to play here this season. We were fortunate to win."
The Blues, held to a draw by third-tier Brentford in the FA Cup, had to wait until first-half stoppage-time before taking the lead at the Madejski Stadium, with a neat pass from Fernando Torres setting up his fellow Spaniard Juan Mata.
Frank Lampard, repeatedly linked with a move away from Chelsea despite impressing yet again this term, made it 2-0 in the 66th minute when he rose above the Royals' defence to head in a corner.
But Le Fondre increased the pressure on Chelsea interim manager Rafael Benitez with two well-struck goals in the final three minutes.
"You might not have seen that coming, but we have done it here before," said Reading manager Brian McDermott. "If you have got Adam Le Fondre at your club, you always have a chance."
Meanwhile a dejected Benitez, who kept Chelsea captain John Terry on the bench, added: "The atmosphere was not good in the dressing room. It is very difficult to take."
Arsenal also came from 2-0 behind at home to Liverpool to force a 2-2 draw that did little for the top four ambitions of either club.
Defensive mistakes by the Gunners led to Liverpool goals for Luis Suarez and Jordan Henderson.
But within a few minutes of Henderson's goal on the hour, Arsenal were level.
Olivier Giroud headed in Jack Wilshere's free-kick and the Frenchman then turned provider for Theo Walcott, who equalised with a powerful shot.
"We were outstanding going forward but nervous defensively," said Arsenal manager Arsene Wenger.
"I think recent accidents against Manchester City and Chelsea affected the heads of the players. But we showed quality and spirit to draw."
Tottenham remained fourth thanks to Gareth Bale's superb leveller in a 1-1 draw away to Norwich.
The Canaries, fresh from the embarrassment of being knocked out of the FA Cup by non-league Luton, went ahead when Wes Hoolahan turned in Anthony Pilkington's 32nd minute cross.
But Wales winger Bale struck in the 80th minute when he collected the ball inside his own half, ran at the defence and curled a shot across the goalkeeper.
"For the people who think I am diving, Alexander Tettey caught me, but I stayed on my feet and scored with a good finish," said Bale.
Fifth-placed Everton closed to within a point of Tottenham after a 2-1 win at home to West Bromwich Albion.
Leighton Baines gave Everton a 29th minute lead at Goodison Park and doubled their advantage on the stroke of half-time with a penalty after Victor Anichebe was fouled in the box.
Shane Long pulled a goal back for the Baggies with a 65th minute header.
Meanwhile Fulham beat London rivals West Ham 3-1 at Craven Cottage.
Bulgaria striker Dimitar Berbatov celebrated his 32nd birthday by putting Fulham 1-0 up with a 10th minute header.
There was a goal rush early in the second half, with Kevin Nolan equalising for the Hammers only for Hugo Rodallega to restore Fulham's lead a minute later.
Joey O'Brien's late own-goal sealed Fulham's victory.