Both sides seemed to understand the importance of this game as the play raged from end to end right from the start with chances being created at both ends.
Within the first five minutes both John Sutton and Jon Daly had come close for either side. But the chance of the opening stages fell to United.
A Paul Caddis cross was flicked on by Paul Dixon into the path of Lee Wilkie, who sent a free header from close range just over the bar.
Lukasz Zaluska was the first keeper called into action, when he did well to block a 15-yard shot from Cillian Sheridan.
But on 23 minutes the keeper was picking the ball from the back of his net.
Maros Klimpl's delightful crossfield ball picked out Jim O'Brien on the left and the winger's cross picked out Sutton unmarked to steer home from close range.
Sheridan should have made it two with only five minutes left to the break.
He was sent clear by Stephen Hughes' throughball and, as he took his time to pick his spot before rolling the ball towards the empty net, this allowed Garry Kenneth to get back to clear.
United made a double change at half-time with Francisco Sandaza and Danny Swanson coming on.
This paid dividends within five minutes when Sandaza bagged the equaliser.
Another Caddis corner caused panic in the Well defence and, after a melee in the six-yard box, the ball fell kindly for the Spanish sub to ram home from close range.
It looked as though United had taken the lead on the hour mark with sub Swanson's calling shot looking netbound.
That was until home keeper Graham Smith pulled off a stunning one-handed save to keep the scoreline level.
With 15 minutes left Motherwell took the lead in controversial fashion as United claimed for a penalty when Klimpl looked to have bundled Swanson over in the box.
The ref waved play on and the ball was cleared to O'Brien at the other end and his cross was headed in at the second attempt by sub Clarkson.
Well could have made it more emphatic when Sutton was sent clear after a sweeping move, but he could only poke wide from 12 yards out.
In the end Motherwell held on for a vital three points in the race for a European spot.