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.
Maryland point guard Melo Trimble, considered a lock to leave the program before struggling in the second half last season, has withdrawn from the NBA draft and will return for his junior season.
Louisville's Chinanu Onuaku, who recently underwent a medical procedure to correct a heart rhythm issue detected during the combine, will keep his name in the NBA draft pool.
Andrew White III will return to the Nebraska men's basketball team next season after removing his name from the NBA draft.