ANN ARBOR—In the highest-scoring game in the history of Michigan football, the Wolverines’ defense came up with the game-winning play.Michael Shaw scored on a 1-yard run, Tate Forcier threw a 2-point conversion to Junior Hemingway and Michigan stopped the potential tying 2-point try in a 67-65 triple-overtime win over Illinois on Saturday.Mikel Leshoure ran for a touchdown to draw the Illini within two. On the conversion try, Michigan put a heavy rush on Nathan Scheelhaase, who flipped a desperation pass incomplete.Michigan (6-3, 2-3 Big Ten) snapped a three-game losing streak and became bowl-eligible for the first time in Rich Rodriguez’s three seasons.A few days after Michigan found out the NCAA would not be coming down hard on the program for rules violations under Rodriguez, the Wolverines came away with a win they badly needed.The Fighting Illini (5-4, 3-3) allowed Tate Forcier to cap an 80-yard drive with a 9-yard, game-tying pass to Darryl Stonum with 1:47 left in regulation.The 132 points made it the highest-scoring game of the year in major college football and in the 131-year history of Michigan football.The last FBS game to produce more points was when Navy beat North Texas 74-62 on Nov. 10, 2007.The previous highest-scoring Michigan game wasn’t nearly as dramatic. The Wolverines beat West Virginia 130-0 in 1904.Denard Robinson threw a 75-yard TD on the first play of the game, but didn’t play after the third quarter and it wasn’t immediately known why he spent the rest of the afternoon on the sideline.Robinson was 10 of 20 for a career-high 305 yards with three TDs and two interceptions. Forcier finished with 12 completions on 19 attempts for 114 yards with two TDs and an interception in the final minute of regulation.Roy Roundtree had a school-record 246 yards receiving and two scores. Hemingway had 104 yards receiving and two TDs.Scheelhaase threw for 211 yards, ran for 101 yards and accounted for four scores. Leshoure ran for 101 yards and a TD and Jason Ford had 91 yards rushing and a score against the 106th ranked defense in the country.But Michigan’s offense is about as good as its defense is bad. The Wolverines rank fourth in the nation and might have been able to reach 60 points in regulation if not for five turnovers.As it was, Forcier led the drive for the tying touchdown that made it 45-all at the end of regulation.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 Patrick Nixon-Youman 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.By rule, the teams had to start going for 2 at that point. Michigan got theirs. Illinois failed to convert and the Wolverines celebrated as if they had clinched a Rose Bowl bid instead of just a trip to some second-tier bowl.It didn’t take long to figure out the game was going to be a shootout.Robinson connected with Roundtree for a score on the first play.He fumbled on his next snap, a teammate recovered the football, then he threw interceptions on back-to-back plays.Michigan’s defense played relatively well in the first quarter — holding Illinois to two field goals — then fell apart, allowing the Illini to score 25 points in the second quarter.The Wolverines were fortunate that their offense kept up, scoring 24 points to make it 31-all at halftime.It was the highest-scoring total in a first half Michigan history, surpassing the 55 points it and Chicago scored in 1939.Michigan had 394 yards of offense in the first half and gave up 312 to Illinois.Shaw’s 18-yard run that put the Wolverines ahead 38-31 midway through the third and Michigan had a chance to take a 10-point lead late in the quarter, but Seth Broekhuizen couldn’t make a 39-yard field goal.Scheelhaase answered with a 27-yard TD pass to Leshoure, who was wide open in the end zone, to tie it on the first play of the fourth.Forcier fumbled on his first play and Illinois turned that into Leshoure’s go-ahead TD run.Forcier, last season’s starter before Robinson took over and become a Heisman contender, led a 12-play drive that tied it.