Howard (10-10, 4-2 Metro-Atlantic) trailed by one with 1:46 left, but Carlton and James Daniel went 7 of 7 from the line, while Bethune-Cookman was 3 of 6 in the same sequence, and Denzel Dulin missed a 3-point attempt with three seconds left.
There were five ties in the second half and a three-point play by Ricky Johnson with 2:06 left put Bethune-Cookman up 39-38.
Travis Elliott's layup and a pair of free throws gave Bethune-Cookman a 25-20 lead with 7:09 left in the first half, but both teams went cold, with Howard going 2 of 10 from the floor and Bethune-Cookman just 1 of 7 through the end of the half, with the Wildcats leading 27-25.
Bethune-Cookman (6-15, 2-5) shot 27 percent and was led by Johnson's 14 points.
The teams combined to shoot 5 of 30 from beyond the arc.