Aplin's 31-yard scoring strike to McKissic shortly before halftime gave the Red Wolves (10-3) a 14-7 lead and Arkansas State allowed only one field goal the rest of the way.
Aplin completed 21-of-30 passes for 213 yards and McKissic finished with 11 grabs for 113 yards as the Red Wolves gained redemption for last year's 38-20 loss in the same bowl game to Northern Illinois.
David Oku scored a touchdown among his 18 carries for 37 yards for ASU.
Spencer Keith went 17-of-33 passing for 157 yards with an interception for the Golden Flashes (11-3).
Dri Archer picked up 77 yards and a score on nine carries for Kent State.