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Southampton had the temerity to score after three minutes at Old Trafford but order was quickly restored with Rooney equalising five minutes later and completing the turnaround with a 27th-minute tap-in.
In the battle for top-four places there was frustration for the main contenders with third-placed Chelsea denied a fifth consecutive away league victory as they let slip a 2-0 lead at Reading to draw 2-2.
Chelsea remain four points clear of Tottenham Hotspur who needed a 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.
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 and three clear of Arsenal.
In a London derby alongside the River Thames Fulham beat West Ham United 3-1.