ANN ARBOR, Mich. (AP) Juwan Howard knew he was getting a hard-nosed point guard when he took over as coach at his alma mater.

In Michigan Wolverines's senior point guard Zavier Simpson, he also saw some of himself.

Howard used astrology to explain his bond with Simpson, who scored 22 points and made big shots late to lift the 19th-ranked Wolverines to an 84-78 victory over Purdue Boilermakers in a double-overtime thriller on Thursday night.

''We both are Aquarius,'' Howard said, adding that Simpson's mom and Howard's grandmother were both interested in astrology. ''We both can be bull-headed, I will also add stubborn.

''We also both are tough-nosed competitors. But the beauty of it is that we both trust one another.''

Simpson did not shoot for more than 18 minutes to start the game but took charge on offense when it was needed.

To avoid a third straight Big Ten loss, the Wolverines (11-4, 2-2) overcame a monstrous effort from Purdue sophomore Trevion Williams, who had career highs with 36 points and 20 rebounds but missed a shot to win at the regulation buzzer.

Williams outplayed Michigan's Jon Teske, making 16 of 28 field goals, while Howard refused to send a double-team to help his senior center.

''I just tried to get him off his feet, get him in the air, get him jumping a little bit,'' Williams said. ''Once I got a couple to fall, I started getting more comfortable and start making more moves.''

Teske scored 18 points and grabbed nine rebounds, and freshman Franz Wagner had 15 points for Michigan. David DeJulius made three free throws in the final minute and finished with 11 points.

But it was Simpson who came up big after a slow start, closing the scoring in regulation and the first overtime, finishing drives to the left with his right hand.

''I seen every one of the Purdue players' heads kind of turn, then I said I got to take it,'' said Simpson, who had nine assists. ''It wasn't more like a selfish thing, it was just a clear lane with no one in the gaps.''

In the first overtime, Eric Hunter Jr. missed a contested jump shot for Purdue (9-7, 2-3), and Simpson's desperation 3-pointer on the run also missed for Michigan at the buzzer.

Michigan left little to chance in the second overtime, scoring the first nine points of the session. Teske had a three-point play, followed by 3-pointers from Simpson and Wagner.

Williams, who went to Henry Ford Academy in nearby Detroit, rushed a shot at the end of regulation while Wagner contested.

It was Williams' sixth double-digit scoring output in the last seven games after he had just one in the first nine. His previous career highs were 18 points and 16 rebounds, both achieved last month at Nebraska.

Williams made a fall-away 3-pointer, his second of the season and third in his career, to put Purdue up 60-58 with 1:28 to go. Simpson answered that one, then the next one, with driving layups.

''He's just a winner,'' Purdue coach Matt Painter said of Simpson. ''He won in high school, and he's won here. Guys that are winners, if they score four or six points, it's no big deal. If they have to score 24, they do.

''That's what winning is about.''

Isaiah Thompson added 14 points and Eric Hunter Jr. scored 10 points for Purdue.

BIG PICTURE

Purdue: The Boilermakers lost another chance for a resume builder, falling to 1-3 against ranked teams.

Michigan: The Wolverines responded to losing two straight Big Ten games, including at rival Michigan State on Sunday, with a hard-fought home win.

BIG MAN DOWN

Purdue junior center Matt Haarms fell awkwardly in the first half and left the game with an unspecified injury. He did not return, and Painter said no update was available after the game.

STILL OUT

Michigan was playing its third straight game without junior Isaiah Livers, who has a groin injury. Livers is averaging 13.6 points per game, second on the Wolverines.

STICKING UP

Howard stood up for former Michigan coach John Beilein when asked about the comments Beilein made to his Cleveland Cavaliers team. Beilein said Thursday he had apologized after using the word ''thugs'' while reviewing film with his players the previous day.

''I understand coach made an apology, so that says a lot about his character,'' Howard said. ''Now, the relationship between coach, his players in Cleveland, that's none of my business.''

UP NEXT

Purdue: Continues a three-game stretch against ranked opponents Sunday against No. 8 Michigan State. After that, the Boilermakers face No. 12 Maryland.

Michigan: In just their fifth conference game, the Wolverines already have a rematch, visiting Iowa on Sunday. Michigan topped the Hawkeyes 103-91 on Dec. 6.

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