ANN ARBOR, Mich. -- Never in 131 years have so many points been scored in a Michigan game. And rarely has a victory against Illinois meant so much to the Wolverines.

In the highest-scoring game in the storied history of Michigan football, the Wolverines' defense provided the game-winning play, stopping a 2-point conversion attempt in the third overtime for a 67-65 victory on Saturday.

Michael Shaw scored on a 1-yard run, Tate Forcier threw a 2-point conversion to Junior Hemingway to put Michigan up 67-59.

Mikel Leshoure ran for a touchdown to draw the Illini within two. On the conversion try, Michigan blitzed Nathan Scheelhaase and he could only flip a desperation pass incomplete.

"The defense made a play -- a fitting ending," said Michigan coach Rich Rodriguez, who for the first time in three years as Wolverines coach as a bowl-eligible team.

Michigan's season almost assuredly will not end against rival Ohio State. For college football's winningest team, that's a big deal right now.

"I feel like a weight has been lifted off of our shoulders," Michigan linebacker Craig Roh said.

Michigan (6-3, 2-3 Big Ten) snapped a three-game losing streak that was making this season feel a lot like the past two, when Rodriguez managed only three Big Ten victories.

That the win came a few days after Michigan found out the NCAA would not come down hard on the program for rules violations under Rodriguez made it even sweeter for the coach.

"It's been a good week," Rodriguez said with a grin.

In a game in which the offenses were all but unstoppable, the Fighting Illini (5-4, 3-3) didn't go for it on fourth-and-1 from their 42 against one of the nation's worst defenses. Forcier took advantage, capping an 80-yard drive with a 9-yard, game-tying pass to Darryl Stonum with 1:47 left in regulation.

"I thought about it," coach Ron Zook said, "even though punting was the conventional play."

Nothing about the thriller at Michigan Stadium was conventional.

The 132 points made it the highest-scoring game of the year in major college football and in the history of the Big Ten. The teams combined for 1,237 yards of offense, 676 for Michigan.

"That's not easy on the heart," Rodriguez said.

The previous highest-scoring Big Ten game also involved Michigan. The Wolverines shut out Michigan Agricultural College -- now known as Michigan State -- 119-0 in 1902.

The last FBS game to produce more points was on November 10, 2007, when Navy beat North Texas 74-62, according to STATS, LLC. The previous Michigan record for total points wasn't nearly as dramatic, beating West Virginia 130-0 in 1904.

Denard Robinson was 10 of 20 for a career-high 305 yards with three TDs and two interceptions and ran for 62 yards, but didn't play after the third quarter.

"He was dizzy and had a headache," Rodriguez said.

Forcier finished with 12 completions on 19 attempts for 114 yards with two TDs and an interception in the final minute of regulation.

Michigan's Roy Roundtree had a school-record 246 yards receiving and two scores. Hemingway had 104 yards receiving and two TDs.

"Our wide receivers made a lot of big plays," Rodriguez said. "That may have been the difference in the game."

Scheelhaase threw for 211 yards, ran for 101 yards and accounted for four scores. Leshoure ran for 120 yards and three scores and caught two TDs. Jason Ford had 91 yards rushing and a score against the team that entered the game with the 106th-ranked defense in the nation.

"It's fun to score like that, but you want to win the game," Leshoure said.

Michigan's offense is about as good as its defense is bad. The Wolverines rank fourth in the nation in total offense and might've scored 60-plus points in regulation if they didn't have five turnovers.

As it was, Forcier led the drive for the tying touchdown that made it 45-all at the end of regulation.

"We had plenty of opportunities to win the game, and we never made a play," Illinois defensive coordinator Vic Koenning said.

Every overtime possession resulted in a touchdown.

Shaw's 5-yard touchdown run in the first overtime put Michigan ahead, then Leshoure's run converted a fourth-and-1 and forced a second overtime.

Scheelhaase then threw a 25-yard pass to a wide-open Leshoure for a one-play possession, but Forcier answered with a 9-yard TD pass to Hemingway that was deflected by defensive back Terry Hawthorne -- sending the game to a third OT.

"That was a lucky break," Rodriguez said.

By rule, the teams had to start going for 2 at that point. Michigan got theirs and Illinois failed.

"This is absolutely deflating," Zook said. "If anyone doesn't think this is deflating, they shouldn't even get on the plane home."

The Wolverines, meanwhile, celebrated as if they had clinched a Rose Bowl bid instead of just a trip to a second-tier bowl. Forcier jumped and screamed as he ran off the field, then slapped hands with fans along the tunnel before racing to the locker room.

Michigan athletic director Dave Brandon said he put his arm around Rodriguez as they walked to the embattled coach's news conference.

"I said, `You had a good week, Coach,' and he did," Brandon recalled. "It's been a month since we had a win and the [NCAA] situation is over, and I think Rich was to a degree was vindicated. Now, we're going to a bowl and if we can find ways to win, it'll improve the picture."