OSU starting quarterback J.T. Barrett left the game with a leg injury midway through the third quarter and did not return.
Saturday's loss was the Wolverines' sixth straight to the Buckeyes and 13 in the past 14 meetings.
Barrett's run cut Michigan's lead down to one score, 14-7, with 9:50 to play in the first half.
Three years ago, Barrett was injured against MI and Cardale Jones took over. He also ran for 67 yards and a touchdown.
Down to its third-string quarterback, John O'Korn, Michigan came out hot in the first quarter, jumping out to a 14-0 lead with creative early play-calling and a smothering defense.
Red-shirt freshman Dwayne Haskins Jr. led the Buckeyes right down the field to give Ohio State the lead and the eventual win, 31-20.
He was tackled by Wolverines linebacker Mike McCray with 6:07 left in the quarter and his team trailing 20-14.
8 Ohio State at noon.
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Barrett, a senior, was just three of eight for 30 passing yards and a touchdown. MI rushed the ball 36 times for 100 yards.
Ohio State successfully possessed the ball, running for 84 yards in the fourth quarter.
The ensuing extra point game the Buckeyes a 21-20 advantage over MI.
Here's how to watch Ohio State vs. MI online. However, before the Buckeyes could get off a snap, they were twice penalized for false starts.
Two plays later, Haskins called his own number, rushed around right end and gained 22 yards before being pushed out at the one-yard line.
On the Buckeyes' next drive, he drove the team 47 yards to set up a 44-yard field goal that extended the lead to 24-20.
The Wolverines had an answer in the third quarter when Karan Higdon capped a 51-yard drive with a 2-yard scoring plunge, but Quinn Nordin's extra point was blocked.