In truth, Sutton profited from a mis-hit shot by David Clarkson but his finish was clinical and sealed the points.
His late goal ended a miserable week for Hibs at Easter Road, following their exit from the CIS Cup at the hands of Morton last Tuesday.
It was Hibs that started brightly and Graeme Smith went down bravely at Dean Shiels' feet as he ran on to Steven Fletcher's pass.
And the Motherwell keeper kept his side level with a fine block from Shiels in the fourth minute after a clever flick from Fletcher.
Yves Makaba-Makalamby had a lucky escape when he dropped Sutton's cross, but the keeper did well to clear from Chris Porter after the striker slipped away from Martin Canning.
There was lots of neat passing but no end product as John Rankin fired wide from 20 yards and Colin Nish nodded Shiels' cross over the bar.
Hibs' defence backed off Stephen Hughes allowing him to hammer in a 20-yarder that Makalamby fisted away.
But Hibs finished the first half stronger, Shiels neat run carried him clear of Paul Quinn and Stephen Craigan, but his attempted lob was a weak finish to the build-up play.
Fletcher did have the ball in the net after 44 minutes when Shiels and Joe Keenan combined well but he was narrowly offside as he headed home and Motherwell went into the break level.
But it was the visitors who blew a great chance five minutes into the second half. Sutton timed his run to perfection, but somehow head Quinn's cross over the bar from six yards.
And Motherwell had a penalty claim turned down as Canning went through Porter before Makalamby raced out to save from Keith Lasley with his feet.
But the key moment came after 79 minutes as Clarkson's miscued shot fell to Sutton six yards out.
Canning lost his footing as the striker turned and he was able to fire high into the top corner past Makalamby to win the game for Well.