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.
Mississippi State freshman guard Malik Newman will withdraw from the NBA draft, but sources told ESPN he might explore other opportunities besides returning to Mississippi State.
Seton Hall sophomore Isaiah Whitehead will stay in the NBA draft and not return for his junior season.
Washington State's trio of Josh Hawkinson, Conor Clifford and Ike Iroegbu have withdrawn from the NBA draft and will play their senior season with the Cougars.