Wright, a walk-on, also had 12 rebounds for the Hawks (11-15, 6-10).
It was the last game of the season for Morgan State (7-20, 6-10), which is on probation and not allowed to play in the conference tournament.
UMES had six players in double figures, led by John Woods' 20 points.
"This was a very big win for us," UMES coach Jeff Menday said. "This was a must win and our guys stepped up and accepted the challenge. Morgan State came in with nothing to lose and everything to gain and it showed because they played very tough."
The Bears rallied with three three-pointers, two by Chris Watson, to regain the lead at 87-85. UMES recovered on a layup by Woods to tie it at 87.
A three-pointer by Jason Demory put the Bears up at 90-87, but Woods scored to cut the margin to one point. Wright then scored while being fouled and put UMES ahead, 92-90.