Mershon's key basket with 21 seconds left snapped a 2-minute scoreless spell down the stretch for Drexel (28-10) and put the Dragons up by a point.
Mershon finished with 14 points and eight rebounds. Taylor Wootton added a game-high 16 points and six rebounds.
The Utes (23-14) were paced by Iwalani Rodrigues with 12 points.
Michelle Plouffe supplied nine and 14 rebounds for Utah.