Victory took Stuart McCall's side level on points with second-placed Inverness ahead of their game with Partick on Sunday, after teenage substitute Craig Moore equalised Ryan Stevenson's opener for Hearts with a stunning strike.
In contrast, defeat for the Edinburgh side was exacerbated by victories for fellow strugglers Kilmarnock and St Mirren to leave them 13 points adrift.
The game slowly sparked into life after a cagey start, with Well twice frustrated by penalty appeals for handball that failed to impress referee Brian Colvin.
Jordan McGhee blocked an Iain Vigurs shot before Danny Wilson appeared to move his hand in the direction of Henri Anier's cross but Colvin was unmoved on both occasions.
Vigurs also tried his luck with a couple of long-range shots before Hearts created the best opportunity of the opening 45 minutes.
Gunnar Nielsen, making his home debut in the absence of the injured Lee Hollis, came out to block Jamie Walker's strike before the keeper recovered to tip David Smith's follow-up effort over the bar.
Motherwell improved after he break, with striker John Sutton heading just wide before Hearts stopper Jamie MacDonald pushed another round the post.
Hutchinson then saw a header cleared off the line by Callum Tapping and Sutton hooked the rebound wide of the mark.
Gary Locke's side then made Well pay for their inability to convert chances into goals as they took the lead through Stevenson.
The midfielder collected a ball from sub Scott Robinson before advancing into the box and firing a deflected shot past Nielsen at his near post after 62 minutes.
But the lead did not last long, 19-year-old Moore grabbing the equaliser in spectacular fashion just 30 seconds after coming on as he fired a 22-yard into the top corner on 69.
The home side pushed for the winner and it duly came courtesy of Hutchinson seven minutes from time as he headed a Vigurs corner down and over the line from six yards.