With Kris Gulley making back-to-back jumpers, the Golden Panthers (5-3) went on a 12-0 run midway through the first half. Baskets by Draper and Mavin gave FIU a 22-11 lead before the Owls (3-5) ended an 11-minute drought.
It was 28-15 at the half and reached 25 late in the second half.
Yonel Brown led Kennesaw State, which shot just 27 percent (19 percent in the first half), with 16 points. The Owls were just 4 of 21 from 3-point range.
Mavin grabbed eight rebounds as FIU had a 44-34 advantage on the boards. The Panthers made 43.6 percent from the field despite hitting just 2 of 13 3's. They also struggled from the free throw line, going 9 of 19.