Scott Severin and Sean Dillon both bundled the ball into their own net either side of David Goodwillie's penalty equaliser.
But the home side were well worth their victory as United struggled to cope with their attacking play.
Severin's own goal came after just 50 seconds as the centre-back endured a disastrous start.
The former Aberdeen captain committed himself inside the Motherwell half following Tom Hateley's clearance, allowing Alan Gow to run at the remaining United defenders.
Gow, making his first SPL start for Motherwell, slipped the ball through for Nick Blackman, who set up the unmarked Jamie Murphy as he cut in from the left.
Dusan Pernis palmed out Murphy's low drive from but the ball hit Severin and went over the line.
The visiting defence continued to look vulnerable as Motherwell searched for a second goal.
Garry Kenneth was beaten inside the box by both Blackman and Chris Humphrey in the space of two minutes but the resulting crosses just failed to fall for a claret and amber shirt.
Pernis pushed wide Murphy's low drive and then produced an even better save to parry Gow's powerful 20-yard strike, before Steve Jennings fired just over from similar range.
Motherwell suffered a blow in the 20th minute when Keith Lasley limped off with what appeared to be a hamstring injury. Steven Saunders came on at right-back and Hateley moved into midfield.
The stoppage disrupted Motherwell's flow and Darren Randolph made his first save in the 28th minute when he held Jon Daly's acrobatic volley following some route-one football.
But Pernis was soon called into action to save Murphy's drive and United also lost a player when Craig Conway limped off in the 35th minute, with Barry Douglas coming on at left midfield.
Gow almost connected with Hateley's inswinging free-kick as Motherwell started the second half well but they gifted United a 50th-minute equaliser.
Stephen Craigan misjudged a high ball following a long throw-in and cleared the ball with an arm. There were few protests when Steven McLean pointed to the spot and Goodwillie sent Randolph the wrong way.
Motherwell tried to hit back quickly and Gow was causing problems with his quick feet on the edge of the box, but two shots failed to test Pernis and he over-hit a pass to Murphy with the winger in a good position.
Motherwell continued to threaten and Pernis had to dive at full stretch to push away Murphy's curling effort.
The home side were rewarded for their ambition in the 75th minute with the second own goal of the game. Hateley found Humphrey in space on the right wing and his driven cross was turned home by Dillon as Gow and Blackman tried to convert.
Saunders headed over from six yards after getting a clean run at Humphrey's corner as Motherwell comfortably saw out the win.
United never looked like forcing another equaliser and will have to improve considerably when they return to Fir Park on Tuesday in the Co-operative Insurance Cup quarter-finals.