Tom Hateley came close to a second for the visitors, his shot well saved by goalkeeper Cammy Bell.
The Fir Park team increased their advantage midway through the first half when Jamie Murphy headed Tom Hateley's centre past Peter Enckelman.
Well's Darren Randolph saved a fine Chris Maguire low shot before Shaun Hutchinson converted Tom Hateley's corner ahead of the late Dons goal.
"The game plan revolved around Tom Hateley and unfortunately he was violently sick during the game and then at half-time, " Young told BBC Scotland.
McCall had recalled Tom Hateley and Sutton, while on-loan Blackburn defender Gavin Gunning was handed a first start in place of the injured Stevie Hammell.
Midfielder Tom Hateley, who was named Motherwell fans young player of the year at a ceremony on Saturday, could also soon pledge his future to the club.
The first half ended with both teams making enforced substitutions, Naismith limping off to be replaced by John Fleck and the winded Tom Hateley making way for Sutton.
Murphy ghosted in behind the Hibs defence to meet a Tom Hateley cross early in the second half but the forward could not convert from a tight angle.
Craig Thomson's last-ditch tackle to prevent Lukas Jutkiewicz latching on to Tom Hateley's through ball merely delayed the opening goal as Motherwell took the lead from the resulting corner.
The Northern Ireland forward made no mistake, however, when he stole in front of Tom Hateley to stab home a volley from 10 yards following a fine Steven Naismith cross.
Tomas Cerny denied Motherwell's Tom Hateley from the spot just before the half-time interval after Martin Canning had felled Nick Blackman, but Hamilton held out to take all three points from the narrow victory.
And Motherwell moved further ahead when Sutton and Marius Zaliukas rose to challenge for Tom Hateley's lofted free-kick and the striker claimed the last touch as the ball found its way into the net.
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