Javoris Bryant added 11 points for the Wildcats (14-11, 8-3), who won for the first time in three games.
Delaware State (9-14, 5-6), which has lost five of its last six games, was led by 12 points from Marques Oliver, the only Hornet to score in double figures.
The most significant part of the game included the final 8:57 of the first half through the first 4:25 of the second period, as the Hornets went without a field goal for those 13-plus minutes.
During that stretch, Reed led the Wildcats on a 27-3 run. That domination took Bethune-Cookman from a nine-point deficit, 20-11 at 8:57 of the first half, to a 15-point advantage, 38-23 at 16:06 of the second.