RaySean Scott Jr. scored 11 points for the Eagles (21-10, 12-2), who outrebounded the Hatters 42-30 and outscored them 38-22 in the paint.
Christiaan Jones scored 11 points and Divine Myles had eight to become Stetson's all-time leading scorer with 1,827 points, passing Kerry Blackshear (1992-96).
FGCU outshot the Hatters (12-19, 4-10) 45.8 percent to 35 percent and never trailed. Goodwin's layup put the Eagles up 33-26 at halftime and Stetson closed to 33-31 on Rivera's corner 3 early in the second half.
FGCU pulled away on an 18-3 run and led by 24 points on Goodwin's layup with 8:01 left to play.
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