The decisive goal in the first ever meeting between the teams came within moments of kick-off, Inigo Martinez scoring an own goal after the excellent Wayne Rooney had struck the post.
Both sides hit the woodwork thereafter, Real Sociedad on two occasions, but unlike in Saturday's 1-1 draw at home to Southampton in the Premier League, United were spared the pain of shipping a late equaliser.
"I thought we played well tonight. I thought we created opportunities," said United manager David Moyes.
"But while it was 1-0, I still had feelings of Saturday left inside me and while it was 1-0, you know you can always lose a goal from a corner kick or a free-kick. "But it wouldn't have been right if we hadn't taken all three points tonight."
Victory, coupled with Bayer Leverkusen's success against Shakhtar Donetsk, leaves United a point above the German side at the top of Group A ahead of their return fixture against La Real on November 5.
"It makes life difficult when you go 1-0 down so early on," said visiting coach Jagoba Arrasate, whose side have lost their first three games. "You have to say it's a fair result."
Amid domestic shortcomings, the win also eased some of the pressure on Moyes, whose storied predecessor, Alex Ferguson, was once again in attendance, a day after launching his new autobiography.
With Robin van Persie carrying minor toe and groin injuries, Javier Hernandez was handed a start up front for United, while La Real recalled captain Xabi Prieto following a spell out with hamstring trouble.
United were trialling a new 'singing section' in the East Stand and the 1,500 fans in that area were given something to sing about within only 69 seconds of kick-off.
Rooney left three defenders in his wake with an uncharacteristic jinking run on the left-hand edge of the penalty area and although his shot hit the post, Martinez inadvertently shanked the rebound into his own net.
Rooney was one of several players criticised in Ferguson's book, with the Scot repeating his allegation -- contested by Rooney -- that the striker asked to leave the club in May, but he was at the heart of every United attack.
He had a volley saved by Claudio Bravo and then volleyed acrobatically over the bar from an Antonio Valencia cross, while Hernandez saw a header disallowed for offside.
The visitors began to threaten on the break, however, and after David de Gea tipped a Haris Seferovic shot over, Antoine Griezmann almost silenced the stadium with a free-kick that bounced back off the left-hand upright.
The scares continued early in the second half, with Jonny Evans slicing a cross from Seferovic inches over his own bar in the 51st minute.
Bravo had to produce a sharp save to block a Phil Jones header from point-blank range, but in response, Alberto de la Bella almost embarrassed De Gea with a cross-shot from close to the left-hand touchline that hit the near post.
Rafael ceded his place to Chris Smalling with half an hour to play, apparently due to injury, but gradually United began to reassert control.
Valencia and Rooney each shot straight at Bravo, before the latter produced a piercing through ball for the former, whose low effort came back off the foot of the left-hand post.
Only a smart block by Carlos Martinez prevented Shinji Kagawa from tucking away a pull-back from Valencia, before Rooney blazed a half-volley over from just inside the box.
Substitute Ruben Pardo served a reminder of the visitors' threat by bending a free-kick a couple of feet wide.
Bravo had to field a curler from Rooney and then rush out to thwart substitute Ashley Young, but although United could not put the game to bed, on this occasion they did not pay the price.