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.
Indiana guard James Blackmon Jr., who averaged 15.8 points in 13 games before being injured last season, has withdrawn from the NBA draft.
Isaiah Briscoe has decided to withdraw from the NBA draft and will return to Kentucky for his sophomore season. Marcus Lee intends to transfer.
The Big 12/SEC Challenge will again feature Kansas and Kentucky, this time at Rupp Arena. That's not the only exciting matchup in next season's midseason conference showdown.