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. The Wolverines also were trying to avenge a 75-52 defeat at Michigan State last month, when questions began in earnest about whether Michigan was tough enough for an extended postseason run.

The perimeter-oriented Wolverines went 0 for 12 from 3-point range Sunday, and had to pull out the victory by forcing turnovers and shutting down the Spartans for much of the second half.

"Today it was all about grit," Beilein said. "We just had to get a win, especially after our Wednesday night disappointment."

The Spartans (22-7, 11-5 Big Ten) had the ball with the shot clock off and the score 56-all, but Burke stole it from Keith Appling near midcourt and went in alone for the game's last field goal.

"I really wasn't pressuring him as hard as I felt like I could, the whole game," Burke said. "I tried to turn him as many times as possible. The one time I did turn him, he kept the ball out, so I just went after it. If I was going to miss it, then I was going to be out of the play."

After Michigan (24-5, 11-5) took the lead, Michigan State's Derrick Nix was fouled with 8.8 seconds left, but he missed the first free throw. He made the second, and the Spartans fouled Michigan freshman Mitch McGary, who missed the front end of a 1-and-1.

Michigan State called a timeout with 4.9 seconds left but never got a shot off. Burke stole a pass by Gary Harris to end the game.

"They switched and it kind of threw us off," Harris said. "We just had to improvise and Trey played good defense and I turned the ball over."

The Michigan State loss clinched at least a share of the Big Ten title for Indiana.

Michigan State had 19 offensive rebounds, but the Spartans also turned the ball over 18 times.

Michigan trailed 31-28 at halftime, but the Wolverines asserted themselves quickly in the second half and led 52-42 when Burke made two free throws with 4:36 to play.

The Spartans rallied, tying it at 56 when Appling made two free throws with 54.8 seconds remaining. After McGary stepped on the baseline, the Spartans had a chance to hold for the last shot — but Appling lost the ball to Burke before Michigan State could even get a play going.

"I'm going to be kicking myself over that for as long as I'm playing basketball that I let that happen," Appling said. "I should've been more aware. I kind of looked to Coach (Tom) Izzo to see if he wanted me to call time out, I turned my head and took my eye off things."

The Spartans have lost three straight — to Indiana, Ohio State and Michigan — and their tough stretch isn't over. They face Wisconsin next.

Adreian Payne had 17 points and Harris added 16 for the Spartans.

Michigan freshman Nik Stauskas played only four minutes — he didn't return after leaving with a cut over his left eye after a scramble for a rebound early in the game.

Freshman Caris LeVert filled in for Stauskas, and his layup in the final seconds of the first half cut the Michigan State lead to three. The Wolverines quickly pulled ahead at the start of the second, drawing three offensive fouls on the Spartans in the first 4:28.

"We knew that Michigan State was going to come in and try to bully us," Burke said. "But we knew if we held our ground, played smarter down the stretch, we have a shot to win the game."