Well began the game like a whirlwind and were rewarded for their enterprising start when they opened the scoring as early as the 12th minute.
Jim Paterson sent David Clarkson through on the left and he played a square ball to Stephen Hughes to fire a low shot past Grzegorz Szamotulski.
The lead was doubled two minutes later as Clarkson worked hard to prevent the ball going out for a goal kick before laying it back to Paterson.
The full-back's cross was perfect for Chris Porter, who rose above the United defence to leave the keeper helpless again.
Well piled on the pressure and made it three on 17 minutes when once again it was a Paterson cross that caused the danger.
This time the keeper saved Porter's header, but the rebound fell kindly for Ross McCormack to smash home from close range.
United made a double change on 25 minutes and the move steadied their ship.
Within 12 minutes they did manage to pull one back when substitute Jordan Robertson rose unmarked to head home a Sean Dillon cross from eight yards out.
Motherwell then made a blistering start to the second half and tied the points up with two goals in the opening 15 minutes.
The first came on 55 minutes when Clarkson rose unmarked to head a McCormack free-kick into the bottom corner.
He bettered that finish only two minutes later after dispossessing Garry Kenneth inside the box before sending a delightful chip over Szamotulski.
United pulled back a couple of goals in the final 15 minutes.
The first came when a Willo Flood cross from the right was mis-hit by a Well defender and struck Noel Hunt on the chest before bouncing over the line.
In stoppage time United added a third when Craig Conway's cross was met by the head of Hunt, who managed to nip in front of keeper Smith.
This did not take the edge of a fine win for Well, who moved six points ahead of United in third place.