ANN ARBOR, Mich. — It was exactly the type of game that John Beilein’s Michigan team had seemed incapable of winning.

The Wolverines missed every 3-pointer they took and were stuck in a bruising struggle against a physical Michigan State team. Then, in the final minute, Trey Burke made perhaps Michigan’s biggest play of the season — on defense.

Burke’s steal and dunk put the Wolverines ahead by two with 22 seconds remaining, and fourth-ranked Michigan held on for a pulsating 58-57 win over No. 9 Michigan State on Sunday. Burke had 21 points and eight assists, and he kept the Wolverines from collapsing after they blew a 10-point lead in the final minutes.

“It would have been a shame to lose that one,” said Beilein, Michigan’s coach. “We haven’t had a lot of adversity this year, and that’s why it’s been magnified over this past month.”

Once ranked No. 1 in the nation, Michigan was coming off a stunning loss at Penn State on Wednesday night.