Midweek injuries ruled Rory McArdle and Zander Diamond out of the Dons defence, with Michael Paton and Magennis also dropping out and Nikola Vujadinovic, Ryan Jack, Sone Aluko and NickBlackman coming in.
Tomas Cerny denied Motherwell's Tom Hateley from the spot just before the half-time interval after Martin Canning had felled NickBlackman, but Hamilton held out to take all three points from the narrow victory.
Bougherra and David Weir got in each other's way as they both tried to make a headed clearance and the ball ran loose for Sutton to squeeze in a shot and the ball crossed the line before NickBlackman could claim the goal for himself.