Potts, who played all 40 minutes, hit just 5 of his 17 shots but made 10 of 11 at the free throw line while Moody finished a much more efficient 9 of 16 from the field.
The win snaps an eight game losing skid for the Wildcats (5-12, 2-1 MEAC) and was their first road win since November 16, an 86-79 win over Tennessee Martin.
Jeff Short hit two free throws for Norfolk State (6-12, 2-1) which tied it at 64 with 2:40 left. But two LaRon Smith free throws and a Potts jumper sparked a 7-0 run for Bethune-Cookman which put the Wildcats in from 71-64 with just 13 seconds left.
Short scored 19 points for Norfolk State. D'Shon Taylor had 13 for the Spartans.