Lennon Miller's late penalty sent Motherwell into the Premier Sports Cup semi-finals and their first date at Hampden since 2018.
Zach Robinson's rocket was cancelled out by Louis Moult, but when Marvin Kaleta was decked inside the box, Miller kept his nerve to convert from the spot.
English striker Robinson bagged his first ever Motherwell goal as he struck a howitzer in first-half stoppage time to take the wind out of United's sails, who had looked to be fairly flying in the first 45.
Robinson's cracker lit up an otherwise dull first half with few genuine chances of note - and the former Dundee man enjoyed it!
But Moult came back to haunt his old side with a late leveller, only for young Miller to score the winner.
While United had looked the more attacking in the first half, they didn't do much with it, but Motherwell hadn't really got going up front until Robinson's rocket - not a bad way to score his first goal for the club.
Motherwell looked better in the second half and took the game to their visitors. They were much more potent up front, with Miller seeing a shot cleared off the line, and Jack Walton forced into some decent saves.
Moult struck late on to level for United and it looked like we were heading for extra-time, until Kaleta was brought down by Luca Stephenson.
Motherwell boss Stuart Kettlewell kept faith with the side that narrowly lost 2-1 at Aberdeen last weekend, though Apostolos Stamatelopoulos was fit enough for a place on the bench.
His Dundee United counterpart Jim Goodwin made one change to the side that lost 1-0 to Rangers on Sunday, with captain Ross Docherty in for Kevin Holt.
United had the first meaningful shot on goal in nine minutes, but Kristijan Trapanovski curled his shot round the top
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