The visitors struck the woodwork either side of half time, while Antonio Valencia also saw an effort come back off the foot of the post in the second half.
Here, Sports Mole takes an in-depth look at exactly how United sealed their spot at the top of Group A.
On target 5
On target 1
Was the result fair?
Yes. United were the better side for the majority of the match and, in truth, probably should have won by more. Sociedad did have their moments, most notably hitting the post twice, but United created more chances and dominated large periods of the game, especially the opening 25 minutes or so. The second half was more even, with both teams playing open, attacking football, but United would have certainly felt hard done by if they came away from this match with anything less than maximum points.
Manchester United's performance
It has certainly not been smooth sailing for United so far this season, but there were plenty of positives to take from tonight's performance. They were rampant at the start of the match and, after weathering a storm at the beginning of the second period, regained control and could have added to their lead towards the end. United never really looked too troubled in defence, with Sociedad's two best moments coming from long-range strikes, and they looked particularly dangerous going forward in the first half. Moyes won't be happy that his side failed to kill the game off when they had the chance, but overall it is a step in the right direction for the Red Devils.
Real Sociedad's performance
They took a while to get going but Sociedad will be pretty pleased with their efforts once they had settled down. They could have been out of the game by the time they started matching United, but the fact that it only remained 1-0 gave them confidence. They were the better team for the first 10 minutes of the second half and looked more dangerous going forward than they had done at any point in the first. They certainly played their part in an entertaining fixture and things could have been different had their two shots that hit the post gone in, but they were still second best on the night.
Sports Mole's man of the match
Wayne Rooney: Without a doubt, the best player on the park tonight was Wayne Rooney. He was instrumental from the first whistle to the last, pulling the strings from his position just behind Javier Hernandez and posing a constant threat to the Sociedad defence. He played a major role in the goal, weaving his way past three or four players into the box before curling an effort towards the far corner that came back off the post, a rebound which led to the own goal. He is in fine form at the moment, and he continued that tonight.
There is only one winner here, too. Following Rooney's dancing feet inside the box, Martinez clumsily put the ball into his own net. There is an element of sympathy for the defender as he had to do something to stop Hernandez having a simple tap in and the ball was at an awkward height, but it was still a bad error and one which, ultimately, cost his side the game.
He improved in the second half, but Bas Nijhuis's first-half display was a shambles. He was handing out yellow cards willy nilly and not allowing the match to flow. The vast majority of his bookings were avoidable, and he seemed to want the headlines all to himself. To his credit, he got two penalty decisions right and calmed down a lot in the second period, but he was certainly the worst thing about that first half.
Man Utd: United will look to get their Premier League season back on track when they host Stoke on Saturday.
Real Sociedad: Sociedad, meanwhile, will be looking for back-to-back wins in the league for the first time this season when they face Almeria on Sunday.