United failed to really get going in West Yorkshire, only coming to life when pulling one back through Marcus Rashford late on, as they fell to their first defeat of the season in all competitions to see the gap on league leaders Manchester City grow to five points.
Huddersfield, defeated 4-0 by Tottenham Hotspur here in their last home outing, were happy to sit back and soak up the pressure in a change of ploy from that recent loss.
Just when United were starting to grow more into the game, seeing Lukaku send an overhead kick narrowly wide of the target, Huddersfield struck for the first of their two goals.
The former Derby County winger had his shot well saved by David de Gea but Mooy was there to tuck home the rebound, becoming just the second different player to net against the Red Devils this term and ending his side's 10-hour wait for a goal in the process.
The second goal also came from an individual mistake as Victor Lindelof, the man brought on to replace Jones in the heart of defence, failed to get his head to a high ball over the top and Depoitre was gifted the chance to round De Gea and roll it home.
United continued to see more of the ball in the remainder of the first half and perhaps should have had a route back into the match, only for Mason to wave away strong appeals for a penalty when Elias Kachunga barged into Ander Herrera.
Ashley Young, doing more than any other United player to drag his side back into the match, was wayward with his sliced attempt from 20 yards as the title chasers continued to be frustrated.
With a quarter of the match left to play United still had just the one Lukaku shot on target to show for their attacking efforts, as they headed towards successive league games without scoring a goal.
They avoided that feat courtesy of a close-range header from Rashford, though, as he ghosted in to convert a right-sided cross from strike partner Lukaku 12 minutes from time.
Nearly half of United's goals this term have come in the final 10 minutes of games, and it was Mourinho's men who were asking all the late questions.
That one final killer chance they craved arrived in added time, but Mathias Zanka dived in front of Chris Smalling's goalbound shot to help Huddersfield see things through for a first win in this fixture since March 1952.