Wayne Rooney did all the hard work to create the second-minute opener and watched as his shot crashed off the far post and into the path of Martinez who inexplicably directed the ball into his own net.
United failed to capitalise on their Rooney-inspired dominance, giving Sociedad confidence they could still get something from the game but despite twice hitting the woodwork the La Liga side left empty handed.
Victory gives United seven points from three matches, while Sociedad have yet to pick up a point and look highly unlikely to progress from the group.
United had aimed to create a noisy atmosphere at Old Trafford by trying out a new 'singing section' of the stadium but they did not need it as their flying start raised the decibels from the off.
Rooney's skill in weaving his way past several defenders fully deserved a goal and while his blistering shot crashed against the far post, an apparently panic-stricken Martinez was on hand to turn the rebound into his own net.
Watched by former manager Alex Ferguson, who has grabbed all the headlines in the build-up to this match following the release of his autobiography, David Moyes' men did as much as they could to try to turn the spotlight back on them.
Rooney went for the spectacular with an overhead kick that would have been like the goal of the season he scored against Manchester City in 2011 but it flew well off target, while Javier Hernandez had a header disallowed for offside.
The visitors finally tested United keeper David De Gea half an hour into the game when Ryan Giggs was dispossessed by Haris Seferovic near the halfway line and the Sociedad striker charged forward and his shot from 25 metres out was tipped over the bar.
Sensing an opportunity, with United having failed to stretch their lead despite their early dominance, Sociedad went close again just before halftime when Antoine Griezmann smashed a free kick over the wall and against the post.
United, whose teamsheet had featured the surprise omission of striker Robin van Persie who Moyes later said was struggling with some knocks, started the second half with Phil Jones forcing a save from Claudio Bravo to keep his header out.
The hosts then hit the far post with a low Antonio Valencia effort shortly after Sociedad had left De Gea raising his eyebrows in surprise that a cross from Alberto de la Bella had rattled his bar.
United, only too aware that a one-goal lead is too slender having conceded in the 89th minute at home to Southampton in the Premier League at the weekend to draw 1-1, endured a nail-biting end to the match as yet more decent chances went begging.
