Illinois center Nnanna Egwu sank two free throws with 22 seconds left in overtime to give the Illini (12-2) an 80-77 lead. Thirteen seconds later Tracy Abrams sank another and Rayvonte Rice closed it with two free throws with 2 seconds left.
Rice led Illinois with a game-high 29 points and eight rebounds. Abrams had 17 points.
Indiana (10-4) was led by Yogi Ferrell's 30 points.
The Hoosiers led 67-63 with just under 5 minutes to play but had to come from behind on a pair of Ferrell free throws in the final minute to force overtime with the score tied 71-71.
Hoosiers freshman Noah Vonleh finished with 16 points and nine rebounds. But he fouled out with 2 seconds left in overtime.
The final half-minute of overtime was a wild scramble.
Jon Ekey stole a pass from Vonleh in the Indiana lane with 25 seconds to play and Illinois up 78-75. But Rice missed the free throws that resulted from the possession.
Rice fouled Will Sheehey at the other end, Sheehey sank both shots and Indiana was right back in it 78-77 with 22 seconds to play.
But on the next possession Troy Williams fouled Egwu, sending the 6-foot-11 center to the line.
Egwu had been cold most of the afternoon, from anywhere on the court. That included a series of misses on long jumpers. He finished the game 3 of 11 from the field, including 0 of 5 on 3-point shots.
But he sank the two free throws and gave the Illini a tiny bit of breathing room they made stick.
Illinois never trailed in the overtime, and held the Hoosiers to a single field goal, a 3-pointer by Ferrell with 4 seconds to play that pulled them to within a point, 81-80.
But, forced to foul, Indiana had to hope the Illini would go cold.
Rice drew the foul, hit his final free throws and sealed the win.
A back-and-forth first half closed with the teams trading runs that seemed destined to give one or the other an edge going to the locker room. By the time it was over, neither had much of an advantage.
Colbert quickly drew his third foul, sending Vonleh to the line with 1:17 to play in the half.
Groce, after being warned earlier by an official for arguing, didn't like the call on Colbert and was given a technical as he fumed on the sideline.
Ferrell hit both shots, putting the Hoosiers up 36-34.
But Illinois' Joseph Bertrand quickly answered with a smooth jumper and a tie at 36.
Indiana moved up court, settling in to look for the final shot of the half. But Rice cut off a pass, stealing the ball and driving for a layup. Rice was fouled by a stunned-looking Sheehey, and grinned big before he went to the line, hit the free throw and put Illinois back on top, 39-36 with 28 seconds left.
But when the Hoosiers went the other way, it was Sheehey who buried a 3-pointer for a 39-39 halftime tie.