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.
ESPN's Dan Dakich joins The Paul Finebaum Show to discuss the SEC's presence in the NBA Draft.
Ted Kapita was the top-rated recruit from West Virginia in the class of 2015 and recently played at DME Academy in Florida.
With the Suns drafting Tyler Ulis, they now have five guards on their roster who attended Kentucky.