The Spartans (2-6) had not won since beating Life Pacific in the opening game of the season.
The teams swapped the lead throughout as there were 18 lead changes with 16 ties. Bethune-Cookman's Cletrell Pope made a layup for a 65-64 lead with 1:05 left in the game. Steadman quickly answered with a layup to retake the lead. Steadman was fouled when he pulled down a defensive rebound after Leon Redd missed a jump shot. Steadman, who finished with 15 points and 13 rebounds, split a pair of free throws with four seconds left for the final score. Bethune-Cookman's Wali Parks missed a trey as time expired.
Oumar Barry added 13 points and Noah Baumann, who hit three 3s, finished with 12.
Mark Gordon had 16 points for Bethune-Cookman (4-6). Redd was 3 of 9 from distance for 13 points and Malik Maitland added 10.
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