Emmanuel Okoroba and Welsey Dunning added 11 points each to help Hampton (14-15, 11-4 Mid-Eastern Athletic Conference) win its third in a row.
Down 45-34, the Pirates used a 21-6 run to go up 55-51 with 9:51 remaining. Powers made a layup and Ramon Mercado hit a 3-pointer to cap the run. Hampton never trailed again.
Bethune-Cookman (12-17, 7-7) made it 65-63 on free throws from Javoris Bryant with 4:21 left, but the Wildcats made just one field goal the rest of the way, and the Pirates converted eight free throws in the final 2 minutes to seal the win.
The Pirates shot 54.5 percent (12 of 22), compared to the Wildcats’ 35.7 percent (10 of 28), in the second half.
Adrien Coleman had 15 points and 12 rebounds for the Wildcats.