United had gone ahead at the Wankdorf Stadium inside 15 minutes through Cristiano Ronaldo’s third goal in two games since his return, but had a mountain to climb after Aaron Wan-Bissaka was shown a red card five minutes after the half-hour mark.
The Swiss champions, playing in front of a sell-out home crowd, made the most of their numerical advantage after the break to level, with Moumi Ngamaleu equalising on 66 minutes.
The Reds looked to have held out for a point in tough circumstances, but Jordan Siebatcheu pounced on a short back pass from Jesse Lingard to ensure the hosts took the points with the final kick of the game.