Marc Eddy Norelia added 15 points and nine rebounds for the Eagles (7-7), who outrebounded the Explorers 39-29. FGCU is 7-0 when it wins the boards.
Cleon Roberts was 10 of 14 from the field for a career-high 30 points and Jordan Price had 25 for the Explorers (4-6).
Florida Gulf Coast built a 19-point lead behind Simmons' 12 points in the first half but the Explorers shot 55 percent and Price scored 19 points in the second half to keep it a game. Price had a 3-point play with 5:51 left to cut it to six but DeBose quickly answered with a 3-pointer to start an 8-0 surge.
Norelia had 12 points and Zach Johnson had all 10 of his points in the second half for the Eagles.