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.