Stetson (6-14, 4-4 Atlantic Sun) jumped out to a 7-1 lead, used a 9-0 run to push its lead to double-digits with 12:26 left in the first half, took a 36-26 advantage into the break and never trailed.
Kennesaw State, however, scored the first eight points of the second half and Orlando Coleman's dunk with 1:06 to play pulled the Owls (4-17, 1-5) within one, 64-63.
Andrews was perfect from the stripe down the stretch and Myles Hamilton missed a potentially game-tying 3-pointer with 4 seconds left for Kennesaw State.
Delbert Love and Orlando Coleman led KSU with 13 points each.
Colorado State graduate transfer John Gillon has chosen Syracuse, giving the Orange a potential starter at point guard entering the 2016-17 season.
DeSean Murray, who averaged 20.2 points as a sophomore at Presbyterian, will transfer to Auburn to play for coach Bruce Pearl.
Former Kentucky guard Ed Davender, the only Wildcat with at least 1,500 points and 400 assists, has died. He was 49.