The Buckeyes (11-1, 7-1 Big Ten) have won 11 of the past 12 games in what has become a lopsided series.
Elliott's performance came a week after he was held to 33 yards on 12 carries against Michigan State and then criticized the team's play calling and said he will skip his senior season to enter the NFL draft. He had a 5-yard run that put Ohio State up 14-3 in the second quarter, and a 10-yard run put the Buckeyes ahead 35-13 early in the fourth.
Elliott surpassed 1,500 rushing yards for the season, joining Archie Griffin as the only players in Ohio State history with multiple seasons of 1,500 yards. He matched another Ohio State with his fifth career 200-yard game, tying him with Eddie George for most by a Buckeye.
Even with the win, the Buckeyes need Penn State to beat Michigan State (No. 5 CFP, No. 6 AP) later in the day to reach the Big Ten championship game against Iowa. Their fans at the Big House knew it as they chanted: "Go Penn State! Go Pen State!"
The Wolverines (9-3, 6-2) simply could not stop their rival from running at will. They fell behind early, and quarterback Jake Rudock was knocked out of the game when he was sacked and slammed onto his left shoulder.
J.T. Barrett, who had 19 carries for a season-high 139 yards, started the scoring barrage with a 7-yard run late in the first quarter. His 13-yard run late in the third quarter gave the Buckeyes an 18-point cushion, and his 17-yard run midway through the fourth mercifully ended the scoring for Michigan.
As a team, Ohio State ran for 369 yards against a defense that entered the game fourth in the FBS against the run (100.2 YPG allowed).
Barrett was 9-of-15 -- throwing fewer times than he ran -- for 113 yards. A 25-yard touchdown pass to Jalin Marshall capped the first drive of the second half to give Ohio State a 21-10 lead.
Rudock was injured by former high school teammate Joey Bosa early in the fourth quarter and was replaced by Wilton Speight. Rudock and Bosa played together at St. Thomas Aquinas in Fort Lauderdale, Florida.
Rudock was 19-of-32 for 263 yards and a touchdown. Unlike Ohio State, the Wolverines struggled to move the ball on the ground. Three-way player Jabrill Peppers had 29 yards rushing on seven carries, and No. 1 running back De'Veon Smith had 10 carries for just 23 yards.
Michigan kept the game competitive -- in the first half.
Kenny Allen kicked a 25-yard field goal to pull the Wolverines within four points early in the second quarter. Rudock made a 5-yard touchdown pass to Jehu Chesson to cut Ohio State's lead to 14-10 just before halftime.
The Wolverines never caught up. While coach Jim Harbaugh has generated a lot of hype this year for coming back to lead Michigan, where he was the starting quarterback two decades ago, he has to improve a program that is 0-4 against Buckeyes coach Urban Meyer.
This wasn't the year for Michigan to gain an edge in The Game. In the fourth quarter, red-clad fans were easy to see in the emptying stadium and could be heard shouting, "OH-IO! OH-IO!" toward the end of another blowout.
The Associated Press and ESPN Stats & Information contributed to this report.