Rooney, who was the focus of attention before the game following Sir Alex Ferguson's revelations in his autobiography, was at his brilliant best throughout to help United take all three points and move a step closer to the knockout stages of the Champions League.
Rooney was involved in the only goal of the game as after he hit the post the unlucky Inigo Martinez put through his own net early on.
Sociedad twice hit the woodwork, but United really should have won the game more comfortably after wasting several clear chances to score.
The hosts came flying out of the traps and broke the deadlock after just two minutes through an unfortunate own goal from Martinez.
Rooney was the creator of the goal as he weaved his way past a couple of Sociedad defenders and was unlucky to see his shot come back off the inside the post before Martinez inadvertently turned the rebound into his own net.
United continued to call the tune early on and Rooney was denied a second goal on 14 minutes when his left-footed volley from Rafael's cross was well kept out by Sociedad keeper Claudio Bravo.
Rooney appeared to be in the mood and he tried his luck four minutes later with an acrobatic bicycle kick from Antonio Valencia's cross which flew well over the top.
United had the ball in the net for a second time on 20 minutes when Javier Hernandez headed home Ryan Giggs' cross, but the goal was correctly ruled out for offside.
It took until just before the half hour mark for Sociedad to threaten when Giggs lost the ball in midfield and Haris Seferovic picked the ball up and advanced to the edge of the box before firing in a right-footed shot which David De Gea superbly tipped over the crossbar.
Sociedad were inches away from drawing level three minutes before the break when Antoine Griezmann curled a brilliant free-kick from 25 yards out against the post with De Gea well beaten.
United had claims for a penalty waved away three minutes into the second half when Valencia appeared to be shoved in the back by Inigo Martinez, but the home side's appeals were waved away by the officials.
United went close to scoring a second goal on 54 minutes when Shinji Kagawa picked out Phil Jones at the far post and his header was superbly kept out by Bravo.
Sociedad were growing more confident the longer the game went on and Alberto de la Bella almost caught De Gea out with a shot from out wide on the left which smacked the crossbar.
United almost doubled their advantage on 63 minutes when Rooney played Valencia in on goal, but the winger drilled his shot off the post and from the rebound Kagawa saw his follow-up effort blocked by the Sociedad defence.
Kagawa really should have scored two minutes later when Valencia picked him out inside the six-yard box, but he took a touch to many allowing Carlos Martinez to produce a superb block
Rooney wasted a great opening to put the game beyond Sociedad on 71 minutes when he latched onto Valencia's flick-on to go through on goal, but the striker wastefully blazed his shot wide of the target.