Okaro White had 17 points, while Devon Bookert cleared eight boards for the Seminoles (20-13), who will face Georgetown in the next round.
Bernard Thompson finished with 16 points and Jamail Jones chipped in 11 for the Eagles (22-13).
FSU shot 44.4 percent from the field in the opening period as it led 24-19 at the break. FGCU made just 31.8 percent of its field goal attempts in the frame.
The Seminoles connected on 40.7 percent of their field goal tries in the second half and went 10-of-16 at the free-throw line. With 5:22 left to play the Eagles were up one, but FSU went on a 10-4 run to close out the game and seal the win.
FSU outscored the Eagles at the free-throw line, 16-5, although the hosts converted only 57.2 percent at the stripe on the night.