Kennesaw State (5-15, 1-3 Atlantic Sun) was within six with 1:07 to go after a 3-pointer by Yonel Brown and got the ball back on a turnover. But Brown was called for a charge and Tucker added three free throws in the final 25 seconds.
Tucker scored 12 points in the first half when FGCU (13-7, 4-0) took a 42-32 lead. The Eagles led by 14 early in the second half before the Owls got within four.
Kendrick Ray scored a career-high 31 points for the Owls. Brown added 20.
The Eagles had a 39-28 rebounding edge including 13-5 on the offensive glass, plus a 48-28 scoring advantage in the paint.