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The Spanish outfit got off to the worst possible start, as Inigo Martinez sliced into his own net while trying to clear the ball after Wayne Rooney had hit the post in just the second minute of the game.
United threatened once more when Rooney combined with Ryan Giggs in the 21st minute, with the latter providing Javier Hernandez with the opportunity to nod home, only for the linesman to correctly rule the Mexican offside.
The woodwork came to United's rescue once again on the hour mark, with Alberto de la Bella driving at goal from an almost impossible angle, but the upright favoured Sociedad when Antonio Valencia's shot beat Bravo in the 63rd minute.
Shinji Kagawa had the chance to give his team some breathing space when Valencia's cut-back found him at the back post, but the Japanese international decided to take a touch and that allowed Carlos Martinez to get in a vital block.
Rooney missed a glorious chance to put the home fans' nerves to rest in the 89th minute, but the Red Devils saw out a victory which sees them establish a one-point lead over Bayer Levekusen.