Reggie Reid pulled the Eagles to 63-61 with a minute left and then Merrill Holden was fouled at 35 seconds. Holden missed both free throw attempts but on the second, Boykins raced around the back side of the FGCU defender on the left side of the lane, caught the miss in midair and banked the ball in.
The Gulls answered with a Christian Terrell layup but Hamilton made one of two free throws at 21.3 seconds. The Gulls never got a good look at the basket and Terrell's desperation 3 at the end barely grazed the rim.
Erik McCree added 12 points for the Bulldogs (9-2).
Terrell led the Eagles (6-6), who led 36-32 at the half, with 16 points and Demetris Morant had 11 and 10 rebounds.