Johnny Hill had 15 points and seven rebounds for the Redbirds (17-13, 8-9 Missouri Valley), who never trailed en route to ending a three-game losing streak.
Anthony Downing scored 12 points to lead the Bears (9-21, 6-11).
Illinois State led 43-25 at halftime and poured it on in the second half. The Redbirds used a 13-0 run to take a 59-34 lead, a surge punctuated when Carmichael was fouled while converting a thunderous dunk.
During the stretch, the Bears were held scoreless for five minutes. The lead later grew to 30 points at 66-36 after a dunk by Jon Ekey, as the Redbirds' run extended to 20-2 over a seven-minute period.
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.