Bruno Fernandes thought he had given United victory from the penalty spot before the late drama
In a wild and wonderful contest in the Danish capital, United showed guile and grit for periods and twice looked to have claimed a crucial win before succumbing late on to a goal from 17-year-old substitute Roony Bardghji.
They were cruising midway through the first half thanks to Rasmus Hojlund's double against his hometown club - both close-range finishes from a striker knowing exactly where he needed to be and when.
But the game turned in the 42nd minute when referee Donatas Rumsas was called to the pitchside monitor to review a late tackle by Rashford on the ankle of Elias Jelert, and responded by showing the forward a straight red card.
With 13 minutes added, largely as a result of an injury to United defender Jonny Evans and a medical emergency in the crowd, the home side took advantage through Mohamed Elyounoussi's finish and Diogo Goncalves' penalty - awarded for a handball by Harry Maguire.
United defied their numerical disadvantage to hold the home side at bay, before again claiming the lead through Bruno Fernandes' penalty - awarded via VAR for a handball by Lukas Lerager.
But the home side were not to be denied. Lerager made amends and drew them level with a back-post effort, before Bardghji hammered home after United failed to clear.
While United are down, they are not yet out, although they do sit bottom of Group A and face a trip to Galatasaray - where they have never won - before hosting the already-qualified Bayern Munich.
-- Courtesy of BBC Sport