Now the Buckeyes also have a special level of dislike for the Wisconsin Badgers.
"I don't want to go on record saying that I hate Wisconsin more than Michigan," Buckeyes wide receiver Corey Brown said, "but I hate Wisconsin just as much as Michigan."
A lot of that enmity will likely bubble to the surface when the sixth-ranked and unbeaten Buckeyes travel to play the Badgers at Camp Randall Stadium on Saturday.
Blame the antagonism on chippy, close, contentious games the past few years. Each side says the other's fans are obnoxious. Both have accused each other of grandstanding after victories, such as dancing on the opposing team's logo at midfield after a rare road win.
Along the way, they've worked up a heated little rivalry where once there was none.
This year's edition began during the middle of the winter. Wisconsin coach Bret Bielema alleged that Ohio State's Urban Meyer was swooping in and stealing verbal commitments. Both coaches downplay it now. At the time it seemed like a natural extension of the battles that have been taking place on the field.
"We do a lot of recruiting in Ohio. So the kids know each other," Bielema said of the rivalry this week. "That builds up a little bit of animosity and some feelings out there more than anything. I've learned early on in my coaching career you lose more friends in recruiting in the coaching world than you do on game days."
The Badgers have three starters from the Buckeye state, including star linebacker Chris Borland (second in tackles and first in sacks and fumbles recovered), along with tight end Brian Wozniak and defensive lineman Pat Muldoon. Chase Hammond is a backup wide receiver and Darius Hilary is a second-teamer at cornerback as a freshman.
Once just a blip on the schedule, now the game's recent history raises the rancor on both sides.
The Buckeyes won every meeting between 1960 and 1980, and have a 54-17-5 lead in the series. That mark does not count one of the most painful losses ever to the Badgers. Two years ago, the last time the Buckeyes visited America's Dairyland, Ohio State was 6-0 and ranked No. 1 in the nation but David Gilreath returned the opening kickoff for a touchdown and the Buckeyes fell behind 21-3 at the half on the way to a 31-18 loss to the No. 18 Badgers. (Ohio State had to vacate the 2010 season as part of NCAA sanctions for violations committed under deposed coach Jim Tressel.)
"I continually think about when we were ranked No. 1 a couple of years ago going into their house," Ohio State cornerback Travis Howard said. "They took that away. A lot of guys on the team, especially the seniors, are continually thinking about that moment and don't want it to happen again - especially with the perfect season we're having."
Meyer is in his first year at Ohio State as head coach, but has a sense of the emotional tug of war between the teams.
"I'm learning about it. I think they stole a season," he said, referring to the 2010 upset. "(The Ohio State players) were telling me that story a little bit. It's interesting hearing our players talk about it. This is a rivalry game because you have to understand who you're playing and what they've done the last few years."
If you're looking for omens, the week before that Ohio State team's perfect season was ended, undefeated Alabama was No. 1 and was upset - just as it was a week ago by Texas A&M.
Just last year, the Buckeyes broke the Badgers' hearts. Quarterback Braxton Miller danced around to avoid a rush and heaved a 40-yard touchdown pass to Devin Smith with 20 seconds remaining to upset No. 15 Wisconsin, 33-29, in Ohio Stadium.
"It comes up a lot in the players' minds," said Wisconsin's record-setting running back, Montee Ball. "That was a game we felt we could have won and we didn't. We just tell everybody that same thing can happen if we don't go out and execute the way we want to. And way we plan to."
Ohio State has won six of the last 11 meetings and holds a narrow 239-231 edge in points over that span.
Don't expect either side to exchange air-kisses before or after the game.
"I really don't like them, to tell you the truth," Buckeyes defensive lineman Johnathan Hankins said. "I'm sure they probably hate us too, but I really don't care what they think."