"This really hurts," Burke said. "This was for a championship."
The Hoosiers (26-5, 14-4) trailed 71-66 with 52 seconds remaining but took advantage when the Wolverines (25-6, 12-6) were unable to seal it at the foul line.
Jordan Morgan also had a fairly easy tip-in attempt of Burke's miss that could have won it for Michigan, but the ball rolled tantalizingly around the rim and off.
"It just hung there," Burke said.
Christian Watford got to the final rebound Indiana had 23 more boards than Michigan with 4 seconds left and threw it back in bounds to Zeller, ending the game.
Michigan had other opportunities to win Sunday, and two other teams surely wish the Wolverines had.
Ohio State, which beat Illinois on Sunday, needed an Indiana loss to earn a share of the conference championship as did Michigan State, which beat Northwestern later in the night. Sunday's games
• No. 2. Indiana 72, No. 7 Michigan 71
• No 10. Michigan State 71, Northwestern 61
• No. 14. Ohio State 68, Illinois 55
• Temple 84, No. 21. VCU 76
• No. 22. Wisconsin 63, Penn State 60