The reigning Premier League champions had a first-half Inigo Martinez own goal to thank on Wednesday night, as victory over the San Sebastian outfit keeps them top of Group A
United took the lead in rather fortuitous circumstances, as Inigo Martinez lashed the ball into his own net after a dazzling run and shot from Wayne Rooney had bounced back off the woodwork.
The Red Devils failed to extend their lead despite dominating possession, leading to a nervous second period, but held on to claim all three points and cement their place at the top of Group A.
Moyes opted to rest striker Robin van Persie due to niggling toe and groin complaints meaning Javier 'Chicharito' Hernandez was handed an opportunity in attack, while, for the visitors, experienced midfielder Xabi Prieto earned his first Sociedad start for a month at the expense of Ruben Pardo.
In addition to Hernandez, Carlos Vela started the match for Sociedad, meaning two of Mexico's top players faced off against one another, although only Chicharito has been featuring for El Tri recently with Vela continuing to turn down call-ups.
The home side had failed to win in its last two appearances at Old Trafford, dropping points against West Brom and Southampton, but any tension around Old Trafford was blown away early on when Martinez put through his own goal to launch a frantic opening period.
Patrice Evra tenaciously won possession on the left flank before Rooney bamboozled Sociedad's defense and unleashed a fierce strike against the upright. Martinez made the worst possible job of attempting to clear, instead diverting the ball into his own net.
Rooney was at the heart of much of United's good work and he drew an excellent reaction save from Claudio Bravo when he met Rafael's 14th-minute cross
Sociedad finally threatened as the half-hour mark approached, with David De Gea clawing Haris Seferovic's deflected effort out of the top corner, and the away team came closer still just before halftime when Antoine Griezmann's 25-yard free kick cannoned back off the underside of the crossbar.
The visitors displayed plenty of intent after the break as the tension at Old Trafford began to ramp up. When a bout of penalty box pinball almost resulted in Jonny Evans putting through his own goal, it became clear that the momentum was shifting.
Phil Jones then powered an unmarked header towards goal from another well-worked short corner to draw a sharp stop from Bravo but, in an increasingly stretched contest, De Gea's crossbar came to his rescue when Sociedad full back Alberto De la Bella skewed a left-wing cross just before the hour.
United then hit the woodwork itself, as Antonio Valencia latched onto Rooney's delightful pass before drilling the ball against the base of the far post. Kagawa saw his follow-up blocked and the ex-Borussia Dortmund player was then denied by a last-ditch tackle from Carlos Martinez as he chose not to strike first time.
Valencia returned the favor to Rooney moments later with a flick-on that his teammate blasted over, before the 27-year-old scuffed a late chance following a whipped delivery into the box. While United failed to add gloss to the scoreline, the result all but ends Sociedad's qualification hopes.