Hyde's 1-yard run with 2:20 to play proved to be the game-winner after the Buckeyes (12-0, 8-0 Big Ten) broke up a 2-point conversion play with 32 seconds to play that would have put the Wolverines (7-5, 3-5) ahead.
Michigan had pulled to within one on a 2-yard TD pass from Devin Gardner to Devin Funchess. The Wolverines outscored Ohio State 20-7 in the fourth quarter.
The victory in Ann Arbor wrapped up an undefeated season for the Buckeyes, who will face Michigan State in the Big Ten title game next week.
Hyde finished the day with 226 yards on 27 carries. Quarterback Braxton Miller completed 6-of-15 passes for 133 yards and two touchdowns, and carried 16 times for 153 yards and three scores.
Gardner passed for 451 yards and four touchdowns and ran for a TD.