Glenn Robinson III made a layup off a feed from Spike Albrecht to give Michigan a five-point lead with 2:07 remaining and the Wolverines then made all six of their free throw attempts the rest of the way to hold off the Hawkeyes.
Robinson had 14 points and nine rebounds, lifting Michigan to 14-4 for the season and to 6-0 in the Big Ten Conference.
The only other team with an unbeaten league record is Michigan State and the Spartans will host Michigan on Saturday.
Both Melsahn Basabe and Aaron White had 17 points for Iowa (15-4, 4-2 Big Ten).
Celebrity Breakups and divorces of 2014 [PHOTOS]