United took the lead through Memphis Depay, however, Pione Sisto ensured that the hosts were going to go in at the break on level terms.
Jesse Lingard struck the bar before Paul Onuachu struck 13 minutes from time to give the minnows a shock lead going into the return leg at Old Trafford next week.
Mixed performances at the back
Sergio Romero (8/10): After David de Gea was struck down by injury in the warm-up, the Argentinian was drafted in, and Romero saved his side's blushes on several occasions. He produced a brilliant one-handed save to keep out Onuachu's strong header.
Donald Love (4/10): No surprise Louis van Gaal introduced Love into the starting XI, and it proved to be a difficult evening for the youngster. Not the best of displays in the first-half, but he will, more than likely, get a second chance in the return leg.
Chris Smalling (5/10): As much as United looked fragile at the back, Smalling, as always, rarely made individual errors. He was playing alongside two youngsters at the back and was to blame for to defence looking out-of-shape.
Paddy McNair (4/10): McNair was all over the place too often in the game, ran ragged by the opposition. Despite him not being on the scene for too long, van Gaal surely has made his mind up on whether the youngster has made it or not.
Daley Blind (6/10): Just like Smalling, Blind rarely made an error in the game, and he looked the safest of the back-four. Enjoyed going forward on occasions, linking up well with the midfield and front line down the left.
Night to forget for midfield
Ander Herrera (4/10): Herrera doesn't appear to be the confident player he once was, looked as though he could have made a mistake at any time throughout the game, and was replaced by Morgan Schneiderlin on 72 minutes.
Michael Carrick (4/10): Carrick was given the captain's armband for the evening and along with Herrera and Mata, it wasn’t his greatest of performances in a United shirt. A languid performance and his mistake led to Midtjylland's equaliser just before half-time.
Not much on offer going forward
Jesse Lingard (8/10): Out of the front three, Lingard was United's brightest spark going forward. All of the forward movement was from the winger and he struck the bar in the second-half. He is definitely one to watch in the forthcoming seasons.
Juan Mata (3/10): Mata has been too inconsistent as of late operating in his more favoured position just behind the front three. Again, he failed to produce anything going forward and was also at fault for Midtjylland’s second after he pulled out of a challenge. Was replaced by Andreas Pereira on 78 minutes.
Memphis Depay (6/10): Memphis has been criticised this season for not showing the reasons why United bought him in the first place. It was one of his better evenings as a United player, scoring the opening goal and it possibly could be something to build on for the upcoming weeks.
Anthony Martial (5/10): A quiet performance from Martial in Denmark, he has produced replica displays this season and gotten away with it, but the goals were supposed to come through the youngster and admittedly he didn’t make the impact he would have liked.