The Wolverines (4-0) took control of the game when they held the Wolfpack (3-1) without a field goal for nearly 10 minutes in the second half.
Michigan reserve Dion Harris scored 14 points. Bernard Robinson and Lester Abram each had 10 points.
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O'Donnell trys to draw foul against Horton
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Julius Hodge led N.C. State with 25 points, eight rebounds and five assists. Scooter Sherrill added 14 points.
Despite winning their first three games, the Wolfpack fell out of The Associated Press poll after being ranked 25th last week.
After N.C. State pulled within one, Michigan took a 53-42 lead with just under seven minutes left. Hodge then ended the Wolfpack's field-goal drought with a three-point play.
The Wolfpack made just enough uncontested layups and Michigan missed enough free throws in the final minutes to allow them to pull within four with 20.4 seconds left, but they couldn't get closer.
The victory gave Michigan coach Tommy Amaker his 100th win, and a 32-31 record in two-plus seasons in Ann Arbor.
The Wolverines improved to 2-1 in the ACC-Big Ten Challenge, and N.C. State fell to 3-2.
Michigan led by seven early, then trailed by nine midway through the first half before leading 33-27 at halftime.