Melsahn Basabe posted 19 points and eight rebounds in the heart-breaking loss for Iowa (10-17, 3-12), which received 14 points from Jarryd Cole. Matt Gatens contributed 13 points and Roy Devyn Marble netted 11 points for the Hawkeyes.
Iowa jumped out to a 32-24 lead at intermission after shooting 52.4 percent from the floor in the first half.
In the second half, Michigan made good on 52.2 percent of its field goal attempts and 14-of-16 free throws to force overtime.
In the extra session, the Hawkeyes missed all five of their shots from behind the arc, sending them to defeat.
Michigan won despite being outrebounded by a 36-27 margin.