After second-placed Manchester City stumbled to a draw at QPR on Tuesday night, it was an evening of opportunity for United, with the Old Trafford club holding on for a 2-1 victory.
They recovered from the early shock of falling behind to a Jay Rodriguez strike, with Rooney rising to the challenge.
"Winning is the name of the game at this stage of the season," said United boss Sir Alex Ferguson.
"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."
Liverpool looked to be cruising to victory at the Emirates when they led Arsenal 2-0 after an hour, before the home side scored twice in three minutes to force a 2-2 draw.
Luis Suarez fired the hosts ahead in the fifth minute with a deflected strike following some poor defending.
And the Arsenal backline was at its shambolic worst again as Liverpool extended their lead after 59 minutes, Jordan Henderson barging through from the right flank to tuck the ball home.
Olivier Giroud kept up his recent excellent form to pull the first goal back five minutes later before laying off a pass from Jack Wilshere into the path of Theo Walcott to drive in Arsenal's second in the 67th minute.
"It was a fantastic game with both teams going for it," said Arsenal gaffer Arsene Wenger. "We have shown great quality and spirit but we were nervous defensively.
"Going forward I felt we were absolutely outstanding all night."
Leighton Baines scored twice as Everton beat West Brom 2-1 to move level on points with fourth-placed Spurs.
The left-back raced forward to collect a pass from Leon Osman and fired into the top left corner as Everton went ahead in the 29th minute at Goodison Park before drilling in from the spot just before the break.
It might have been comfortable for the Toffees after that but for a defensive blunder from Johnny Heitinga, who failed to block Romelu Lukaku's low shot with the ball looping up for Shane Long to head in.
Tottenham, meanhwile, could only manage a 1-1 draw at Norwich, and even that looked beyond them for a long while.
Wes Hoolahan converted Anthony Pilkington's cross to give Norwich the lead in the 32nd minute, but they could not hold it and Gareth Bale produced a superb equaliser after 80 minutes, tearing forward with the ball at his feet before cracking a powerful shot into the left corner.
Third-placed Chelsea were cruising at Reading until two late goals from substitute Adam Le Fondre stunned Rafael Benitez's side, earning the hosts a point from an improbable 2-2 draw.
Juan Mata and Frank Lampard had put Chelsea in charge.
Fulham triumphed 3-1 in their London derby with West Ham at Craven Cottage thanks to goals from Dimitar Berbatov, Hugo Rodallega and a late Joey O'Brien own goal.
Kevin Nolan netted for the Hammers.