The Colonials (13-12, 6-5 Atlantic 10 Conference), who trailed by 12 early in the game, were still down 47-41 with 5:27 to go.
Aaron Ware hit two free throws with 4:48 left to spark the run, which gave George Washington a 58-47 lead with 38 seconds left.
The Minutemen (13-10, 5-5) made only one field goal in the game's final 9 minutes and were held scoreless for 5:06 en route to their third straight loss.
Mikic hit six 3-pointers, while Smith had 14 points and 10 rebounds.
UMass shot 30.4 percent from the field (14 of 46) while George Washington shot 35.3 percent (18 of 51).