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.