Darrin Shine added 11 points for the Hornets (18-11, 15-2 Mid-Eastern Athletic Conference), who had already wrapped up the MEAC regular-season title.
Reserve Aaron Nelson scored 12 points for the Wildcats (8-19, 5-11), who shot 52.6 percent in the first half and led 22-21 at halftime.
Delaware State opened the second half with a 14-0 run to take control. Bethune-Cookman didn't score until Josh Cummings hit a free throw with 11:18 remaining.
But Delaware State never got hot from the floor, shooting 34.1 percent -- including 5-of-23 from 3-point range. Bethune-Cookman rallied and got within 43-40 on a 3-pointer by Jimmy Hudson with 46 seconds left.
Two free throws by Shine and a breakaway dunk by Bluntt sealed the victory.
The Hornets converted 14 Wildcat turnovers into 18 points.