ANN ARBOR, Mich. -- Ohio State followed up its worst with its best.

One week after struggling against Michigan State, the Buckeyes dominated archrival Michigan 42-13 on Saturday to spoil Jim Harbaugh's coaching debut in one of college football’s most storied rivalries.

"I've been very fortunate to be around some big-time games," Ohio State coach Urban Meyer said. "From the bottom of my heart, I told my players that might have been the best one I've ever seen. To come back from the kick in the stomach that we took a week ago; it was an awful week of practice.

"To come out and navigate a storm against an excellent team, especially that defense. ... This is one of the best groups of kids I've ever been around."

Running back Ezekiel Elliott rushed for 214 yards and two touchdowns, and quarterback J.T. Barrett added 139 yards on the ground, 113 yards passing and four total touchdowns.

The eighth-ranked Buckeyes (11-1, 7-1 in the Big Ten) clinched at least a share of the Big Ten East division championship for a fourth consecutive season.

Ohio State was knocked out of the Big Ten championship game next week when Michigan State routed Penn State later in the day.

"To come and execute the way we did today and dominate, it shows how resilient this team is," Elliott said.

Harbaugh, a former Michigan quarterback who tormented Ohio State in the 1980s, was attempting to continue an odd trend. Seven of the previous eight Wolverines coaches won their first meeting against the Buckeyes.

Instead, No. 10 Michigan (9-3, 6-2) had no answer for Ohio State's rushing attack.

"We played faster (than last week)," Barrett said. "We knew they would try to throw the kitchen sink at us. We thought playing at a faster pace would make them tired.

"We could see their defensive line struggling. (Elliott) and myself kept seeing creases, so we ran through them."

The Buckeyes, who have beaten Michigan in 11 of the last 12 meetings, piled up 371 yards rushing and five touchdowns on the ground.

Elliott, one week after a 12-carry, 33-yard performance against the Spartans, approached the school record for rushing yards against Michigan, set by Carlos Hyde (226 yards) in 2013.

"It's a dream come true to be a dominant collegiate athlete," Elliott said. "The offensive line, they've just been so good in my time here.

"That's four straight games the Ohio State offensive line has dominated the (Michigan) game. It all starts there. The chemistry we have with each other has carried us. We play for each other."

Michigan entered the game with the Big Ten's top rushing defense at 79.5 yards per game and was ranked fourth nationally.

However, the tone was set late in the first quarter when Elliott scampered for a 66-yard gain two plays after Michigan roughed Ohio State punter Cameron Johnston.

Barrett capped the drive with a seven-yard touchdown run, his first of a career-high three for the day.

"(Barrett) played his tail off today," Meyer said.

The teams traded scores in the second quarter, with Ohio State leading at halftime 14-10, as the Wolverines took momentum into the locker room after a late touchdown.

"We felt like we could win it at halftime," Harbaugh said.

But the Buckeyes quickly dimmed the positive outlook for many of the 111,829 in attendance at Michigan Stadium.

Ohio State scored on its first four possessions of the second half on a 25-yard pass from Barrett to Jalin Marshall, a 13-yard run by Barrett, a 10-yard run by Elliott and a 17-yard run by Barrett.

"(Ohio State offensive coordinator) Ed Warinner gets blistered, and it's part of the title, but he did a marvelous job," Meyer said.

Michigan quarterback Jake Rudock, who was injured in the third quarter, completed 19-of-32 passes for 263 yards and a touchdown.

The Wolverines could muster only 57 yards rushing on 25 carries. They were limited to 138 yards of offense in the second half after piling up 226 yards in the first half.

"We're not making any excuses; we didn't win the game," Harbaugh said. "We'll regroup. They played better."

NOTES: Running back Ezekiel Elliott is now second all-time on Ohio State's career rushing list, surpassing Eddie George on Saturday. ... Urban Meyer improved to 4-0 versus Michigan as Ohio State coach. ... Michigan hasn't defeated Ohio State since 2011 and has only defeated the Buckeyes once in the last 12 years. ... Michigan honored 44 fourth- and fifth-year seniors during a pre-game ceremony. ... Ohio State co-offensive coordinator Ed Warinner coached from the press box for the first time this season after. … The Wolverines retired five numbers Saturday -- No 48 Gerald Ford, No. 98 Tom Harmon, No. 21 Desmond Howard, No. 87 Ron Kramer, No. 47 Bennie Oosterbaan and the No. 11 worn by Albert, Alvin and Whitey Wistert. ... There was a moment of silence in honor of Chad Carr, the 5-year-old grandson of former Michigan coach Lloyd Carr, who died this week from an inoperable brain tumor.