An own goal from Motherwell’s Louis Laing and a stoppage-time strike from substitute Simon Murray got Dundee United off the mark for the season.
The Tangerines played well at Fir Park and deserved a victory that now sets them up nicely for Tuesday’s Tannadice derby against Dundee.
The visitors looked bright and creative in their passing, while goalkeeper Luis Zwick was outstanding behind a solid defence.
Two changes were made by United from the 1-0 loss to Aberdeen on opening day, with Scott Fraser coming in for his first start in place of John Rankin and Darko Bodul replacing the injured Mario Bilate.
United midfielder Rodney Sneijder missed the game because of virus and he has returned home to the Netherlands to recuperate.
Zwick was called into action on four minutes when he had to dive to push away a well-struck shot from Marvin Johnson.
United gradually grew into the game and Fraser’s strike almost gave them the lead on 33 minutes but keeper Connor Ripley did really well to push the ball away for a corner.
Then, as the visitors continued to press forward, Chris Erskine just missed a Ryan McGowan cross when smack-bang in front of goal.
There was then a big shout for a penalty from the Tangerines when the ball appeared to hit Joe Chalmers’ hand as the ball bounced up inside the box.
With four minutes to go to half-time, a great move by United saw Blair Spittal play the ball infield to Charlie Telfer, who let fly with a shot from 20 yards that was saved by Ripley.
Just before the whistle, another fine Spittal pass reached Erskine but his low shot went wide of the far post.
United started the second half who they finished the first on the attack.
A run down the left from Paul Dixon saw him play the ball into Bodul and the striker’s lay-off was fired over the bar by Spittal.
Telfer had a go at goal from the edge of the box after another intricate passing move from United.
The visitors, backed by an 800-strong travelling support, should have taken the lead on 57 minutes but they squandered what was a fantastic chance.
Erskine was the creator, going on a run before sliding the ball in for Telfer but the midfielder tried to dink it over Ripley instead of blasting it and the goalie saved with his outstretched hand.
Almost immediately, Johnson broke clear for the Steelmen and it needed an excellent save from Zwick with his leg to thwart the sucker punch. The young German was on song again when he forced Chalmers to shoot over the bar from close range.
The Tannadice men were under the cosh at times as the game entered its final quarter but Zwick was doing his bit to keep Motherwell out.
United brought on Robbie Muirhead, Aidan Connolly and Murray for Telfer, Bodul and Erskine as they made a final push for a winner.
Connolly looked lively straight away and did brilliantly to win a tackle in the Well box then sting the hands of Ripley with his snap-shot.
The pressure from the Tangerines finally paid off on 83 minutes when they went 1-0 up.
It was another fine move that saw the ball get played out to Dixon on the left. The full-back took a touch then fired over a superb low cross that was diverted into the net by Laing.
Then came the grand finale from United and, as they broke forward at speed, Connolly played in Murray and the former Arbroath man found the net for his first goal for the club.
Motherwell: Ripley, Hammell, Laing, McManus, Fletcher (Moult 63), Johnson, Lasley, Chalmers (Thomas 66), Law, Leitch (Clarkson 79), McDonald. Subs not used: Twardzik, Kennedy, Cadden, Ferguson.
Dundee United: Zwick, Dixon, Souttar, Erskine (Murray 78), McGowan, Telfer (Muirhead 71), Durnan, Spittal, Fraser, Donaldson, Bodul (Connolly 73). Subs not used: McCallum, Dillon, Rankin, Lochhead.
Referee: Bobby Madden.