Tyler Stone added 13 points, grabbed 10 rebounds and blocked four shots for the Bison (10-10, 4-1 Mid-Eastern Athletic Conference), who trailed 40-32 at halftime.
Howard rallied to a 55-54 lead with nine minutes left, but Jordan Potts scored 12 of the Wildcats' next 14 points for a 68-58 lead with 4:18 to play.
The Bison scored 12 straight points, with a layup by Stone pulling Howard within one and Collins hitting a layup for a 69-68 lead. Stone sealed it with a free throw with 23 seconds left and the Wildcats missed two chances in the final seven seconds.
Diamante Lewis led Bethune-Cookman (6-15, 3-4) with 23 points and Potts added 20 with five assists.