John Davis finished with 10 points and seven rebounds and Four McGlynn added another 10 points for the Tigers (3-1). Keith got to the free throw line for 10 attempts, making eight of them.
Quentin Brewer had 11 points and eight rebounds and Mikel Trapp had 12 points and three steals for the Wildcats (1-3).
McGlynn tallied four of his 10 points at the end of the first half to put Towson up 24-16 at halftime while Brewer contributing five late first half points for the Wildcats. Towson started the second half with a 14-4 run. Keith scored seven of his 10 points in the final half.
Bethune-Cookman shot just 47.1 percent from the free-throw line.