Motherwell manager Maurice Malpas must be wondering how his side lost a match they controlled for long periods.
Collin Samuel volleyed the visitors ahead but were they soon hampered by the dismissal of Christian Kalvenes.
Despite the setback, United doubled their lead when David McCracken headed home from close range.
A Richie Foran penalty and a header from Mark Reynolds pulled Motherwell level, but Noel Hunt was on hand for United to head home the winner.
Motherwell made one change to the team comprehensively defeated by Hearts last week, with Darren Smith making his debut on the right side of midfield replacing Steven McGarry.
United shuffled things around at the back as Stuart Duff dropped to the bench, being replaced by McCracken with Lee Mair moving to right back.
The first chance fell to Motherwell when David Clarkson raced clear, but his shot from a tight angle was blocked by keeper Derek Stillie.
Motherwell continued to press throughout the early part of the game, and both Foran and Paul Quinn had efforts blocked.
United took the lead against the run of play when Craig Conway drove down the left wing and crossed the ball to the back post where Samuel volleyed the ball past Colin Meldrum.
Seconds after taking the lead the Tannadice side were down to ten men when Kalvenes received his marching orders for a second booking after a lunging challenge on Clarkson.
Motherwell began use the extra man to their advantage and Jim Paterson fired in a long range effort which hit the side netting.
In the final minute of the first half however, the visitors doubled their lead when Mair flicked a corner onto the back post where McCracken headed home his first goal of the season.
Although Motherwell tried to force the game in the second period they found it hard to break down the Dundee United defence.
They got the chance to get back in the game from the penalty spot however, as Smith drove into the box before being brought down by Conway.
Foran converted the penalty to claim his twelfth goal of the season.
The goal brought a new sense of belief to the home side and they were shouting for another penalty when Alan Archibald brought down Scott McDonald.
A few minutes later Reynolds bagged the equaliser when he broke clear of his marker to head home form a Paterson corner.
Foran stretched to connect with a Martyn Corrigan cross, but his volley went over the bar as the home team started to turn the screw.
Just as it seemed that Motherwell would go on to win, Barry Robson flicked the ball into the box and Hunt scored with an unchallenged header from the back post, injuring himself in the process.
Motherwell: Meldrum, Quinn (Fitzpatrick 54), Craigan, Reynolds, Paterson, Darren Lee Smith (McGarry 85), Kerr, Corrigan, Foran, Clarkson (Elliot 51), McDonald. Subs Not Used: Graeme Smith, Kinniburgh, McBride, Connolly.
Booked: Paterson.
Goals: Foran 62 pen, Reynolds 68.
Dundee Utd: Stillie, Kalvenes, Mair, McCracken, Archibald, Conway, Kerr, Robertson, Robson, Samuel (Robb 35), Hunt (Goodwillie 81). Subs Not Used: McLean, Duff, Cameron, Kenneth, Smith.
Sent Off: Kalvenes (30).
Booked: Kalvenes.
Goals: Samuel 29, McCracken 45, Hunt 79.
Att: 4,420
Ref: M McCurry