United led at Old Trafford through a Nemanja Vidic header, and while Bastian Schweinsteiger soon got a precious away goal for Bayern, the ailing Premier League champions will have been boosted by the nature of their performance against their much-fancied opponents.
Atletico, meanwhile, hold the advantage going into the second leg of their all-Spanish tie against Barcelona thanks to a brilliant away goal scored by Diego Ribas, although Neymar scored to earn the Catalans a 1-1 draw.
United had an early Danny Welbeck goal disallowed and the England striker then missed a glorious chance to open the scoring when he tried to chip Bayern 'keeper Manuel Neuer when clean through on goal.
The hosts opened the scoring in the 58th minute, Vidic twisting his neck to divert a Wayne Rooney corner from the left into the net at the far post.
Bayern were unable to make it a record eight straight away wins in the Champions League and Schweinsteiger was later sent off after a late challenge on Rooney saw him booked for a second time.
Javi Martinez will also be banned for the return leg at the Allianz Arena next Wednesday.
"I am quite satisfied. Manchester United has one of the best teams in the world," said Bayern coach Pep Guardiola.
"It is always dangerous when you go into the second leg with a 1-1 draw, but even a 2-1 victory would have been dangerous. We will try to win the second leg and I am sure we can do it.
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