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.
Exploding whale video goes viral on Internet
Campus cop fatally shoots Texas student during traffic stop