Coppin State had possession with 30 seconds left and a chance to tie, but a jumper from Keith Shivers fell short.
UMES led by six with 2:06 left in regulation after a layup from Bakari Copeland.
But two free throws from Terry Harris Jr. and back-to-back 3-pointers from Shivers and Joshua Treadwell gave Coppin State a two-point lead.
Dontae Caldwell's layup with a minute left tied it at 77-all, and Harris' jumper at the buzzer missed the mark to send the game into OT.
Caldwell led UMES (6-16, 3-4 Mid-Eastern Athletic Conference) with 25 points on 10-of-12 shooting.
Christian Kessee had 20 points for Coppin State (5-15, 3-4), which had won three in a row after a 12-game losing streak.