Powers' layup with 1:03 left put Hampton (4-5, 2-0 Mid-Eastern Athletic Conference) up 60-55, and Donte Pretlow answered with a basket for Morgan State (1-8, 0-2) with 48 seconds left to cut the lead back to three.
Blake Bozeman made 1 of 2 free throws with 2 seconds left to pull the Bears within two, but Jervon Pressley scored on a putback of his own missed free throw as time expired to cap the scoring for the Pirates. Pressley had 11 rebounds.
Bozeman finished with 15 points and Cedric Blossom scored 14 for the Bears, who shot only 24.6 percent from the field. Morgan State led by one at halftime but fell behind on Hampton's 6-0 run early in the second and never got back in front.