Hill was 6 of 9 from the floor. Carmichael grabbed nine rebounds for the Redbirds (11-9, 2-6 Missouri Valley), who avenged a 77-75 loss to Indiana State in Terre Haute, Ind., on Dec. 30.
Manny Arop led the Sycamores (12-7, 5-3) with 13 points. R.J. Mahurin added nine points and eight rebounds but missed a game-winning 3-pointer at the buzzer.
Jake Odum put Indiana State ahead 53-51 on a jumper with 3:53 left, but that was the Sycamores' last lead. Illinois State scored the next seven points on a Hill layup, a John Wilkins tip-in and three free throws. Odum's two free throws with 6 seconds left pulled Indiana State within 59-58, but the Sycamores could get no closer.
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point guard Melo Trimble, considered a lock to leave the program before struggling in the second half last season, has withdrawn from the NBA draft and will return for his junior season.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.