The fourth-seeded Wolverines failed to score during the final 4:14 of the game after they closed within 63-60 on a 3-pointer by Trey Burke.
Ohio also could not score during that stretch, until Offutt's free throws gave the Bobcats their second major NCAA upset in three years. They opened their 2010 tournament with a victory over third-seeded Georgetown before losing to Tennessee. Ohio advances to a game against South Florida, which backed up its first-round win over California by fighting off fifth-seeded Temple Friday
Michigan has not made it to the second week of the tournament since 1994.
Ohio built a 13-point lead late in the first half and then created one of a series of shocks on the second full day of the tournament. The Bobcats (28-7) joined Norfolk State, a winner over Missouri, and Lehigh, conqueror of Duke, as unlikely participants in the third round.
After Burke's 3-pointer brought the Wolverines within three, they missed their last six shots. Five of those attempts came from 3-point range.
D.J. Cooper made 7-of-11 from the field and led Ohio with 21 points. Offutt added 11 and Ivo Baltic had 10 for the Bobcats, who became the only team from the Mid-American Conference to reach the NCAA after winning the league tournament as the No. 3 seed.
Michigan (24-10), runner-up in the Big Ten, was led by Burke with 16 points and Evan Smotrycz with 15 off the bench.