Sharp scored on a first-period power play and assisted on Patrick Kane's go-ahead tally with 1:19 left in the middle frame for Chicago, which won for only the third time in 16 road games.
Ray Emery turned aside 23-of-24 shots to earn the victory.
Niklas Kronwall got the only goal for Central Division co-leader Detroit, which continued an injury-filled rough patch with a fourth loss in six games.
Jimmy Howard started in net for the Red Wings and had allowed a goal on five shots before the leaving in the first period with a lower body injury.
Joey MacDonald relieved, turning aside 12-of-13 shots the rest of the way.