Jordan Talley's free throw gave the Seahawks a 57-54 lead with 1:03 left in overtime. Evan Bailey's free throws for the Cougars cut the deficit to one with 40 seconds left.
Cedrick Williams and Spruill had the only field goals in overtime, pushing the Seahawks (10-8, 5-2 Colonial Athletic Association) out to a 56-52 lead.
Neither team scored in the final 1:40 of regulation. Talley had the last chance to win it, but his 3-point attempt in the final seconds was off the mark.
The Seahawks overcame 25.8 percent shooting by causing 20 turnovers.
Canyon Barry led Charleston (6-14, 1-6) with 16 points and 10 rebounds.