Albert Abrahams also scored 16 points for the Wildcats (13-9).
The Wildcats, who trailed by six points at 20-14 with 8:38 left in the first half, used a hot-shooting streak by Dukes to go on a 21-5 the rest of the half. Dukes nailed four straight 3-pointers during a two-minute stretch, moving Bethune-Cookman to a 35-25 edge at the break.
The Rams never advanced any closer the rest of the way, with the Wildcats producing their largest lead, 73-45, with 1:49 remaining in the game.
The win was the 99th for Cliff Reed, who is in his eighth year as coach of Bethune-Cookman.