A moment's silence was held prior to kick-off to pay respect to Queen Elizabeth II, who died on Thursday at the age of 96, with UEFA saying in a statement ahead of the match: "UEFA and European football are truly saddened by the passing away of Her Majesty Queen Elizabeth II, one of the world's most-respected figures."
Cristiano Ronaldo, picked as a starter by Erik ten Hag for the first time since United's 4-0 loss to Brentford on Aug. 13, looked to have headed the hosts in front in the 36th minute, but his goal was ruled out for offside.
There was action at both ends of the field, but no goals and the first half ended scoreless, with Ten Hag bringing on Bruno Fernandes for Christian Eriksen and Lisandro Martinez in place of Diogo Dalot at the break.
Sociedad were handed a controversial penalty shortly before the hour when a David Silva shot glanced off Martinez's leg and onto his arm and the referee pointed to the spot. The call for hand ball stood and Brais Mendez beat David De Gea to make it 1-0 to the visitors.
La Real saw out the match to top Group E, while Man United sit in third behind Sheriff Tiraspol, who beat Omonia in their opener.
Sociedad players and their travelling support celebrated wildly at the final whistle as Imanol Alguacil's side secured a first-ever away win against English opposition in European competition.