Ohio State quarterback J.T. Barrett was forced out of Saturday's game against MI with a knee injury, but he suffered it before the game took place.
Barrett later injured his right knee on a run in the third quarter, and watched the rest of the game from the sideline.
MI held the Buckeyes to minus-6 yards in the first quarter. He did rush for 67 yards and a touchdown.
On first-and-goal from the MI one-yard line, Dobbins took the handoff from backup quarterback Dwayne Haskins and pushed the pile at the line of scrimmage into the end zone for his seventh rushing score of the season.
Ohio State coach Urban Meyer has a 6-0 record against the Wolverines, while MI coach Jim Harbaugh is 0-3 against the Buckeyes.
It appears Michigan fifth-year senior quarterback John O'Korn will start for the Wolverines against Ohio State at Michigan Stadium. He stayed down on the field before limping off, and he did not return after he was replaced by Dwayne Haskins.
MI quarterback John O'Korn completed 17 of 32 passes for 195 yards with a touchdown and an interception.More news: India blames Pak for harbouring terrorism
The Buckeyes added onto their lead with a 44-yard field goal from Sean Nuernberger with 10:21 to play in the fourth quarter.
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.
The Wolverines entered halftime tied, but the outcome could have been more favorable after 30 minutes.
Khalid Hill's 2-yard scoring run capped a 13-play, 77-yard MI drive in the opening quarter.
Earlier in the drive, the Buckeyes faced a third-and-two on their own 33-yard line, but Barrett fought his way to a six-yard gain and a new set of downs.
Donovan Peoples-Jones returned a punt 42 yards during the closing seconds of the quarter.
The Buckeyes ran nine offensive plays in the first quarter for a total of minus-6 yards - the first time they have had negative yards in a quarter under head coach Urban Meyer.