Colorado State advances to take on Mike Daum and South Dakota State in the consolation final on Wednesday.
Nico Carvacho had 16 points and eight rebounds for Colorado State (4-1). Adam Thistlewood scored 12, Lorenzo Jenkins 11, and Moore had four assists and five steals and made 8 of 10 shots.
Colorado State closed the first half on a 10-0 run for a 40-32 lead, helped by 15 points off of turnovers.
Carvacho gave CSU a 19-point lead midway through the second half, but FGCU scored 12 of the next 14 and later cut it to four points with 24 seconds left. Masinton-Bonner and J.D. Paige each made two free throws on back-to-back possessions to seal it for CSU.
Haanif Cheatham scored 18 points for FGCU (2-4), which plays UTSA.