Ahmad Walker scored 12 and Stony Brook (17-7, 9-1 American East) shot just 33.3 percent but its defense forced 15 turnovers.
Jordan Reed hit a 3-pointer to give Binghamton a 7-4 lead and the Bearcats pulled away on a 10-3 run to lead 23-18 at halftime.
Stony Brook ripped a 14-2 run capped by a 3-pointer by Coley to go up 32-28, and the lead traded hands seven times until Walker made a dunk and a free throw to give the Seawolves a 47-46 lead at 2:38. Stony Brook pulled away on a 7-2 run for the win.
Reed scored 23 points and grabbed 15 rebounds for Binghamton (4-19, 1-9).