The Hawkeyes (9-10, 2-4 Big Ten) took control of the game with a 12-1 run early in the second half after leading by two at halftime and the cushion helped hold off a late Michigan rally.
Michigan trailed by 13 points late in the game, but pulled within four with 1:22 left after Harris made a four-point play following consecutive 3-pointers from Sims and Kelvin Grady.
Iowa responded offensively and Harris turned the ball over in his backcourt with 1:16 to go, hurting Michigan's comeback chance.
But Grady and Sims kept the Wolverines' hopes alive by making a 3-pointers on consecutive trips down the court, pulling them within three with 39 seconds left.
The Hawkeyes held Michigan off by making just enough free throws and doing a better job of contesting 3-point shots.