ORLANDO, Fla. -- Marquette turned team speed into an early-season upset.
"That was as quick a team that I can recall," Michigan coach John Beilein said. "That's incredible quickness at all five positions."
Darius Johnson-Odom added 14 points for Marquette (6-0), which will play in the tournament championship game Sunday.
"I thought we did a really good job of handling their changing defenses," Marquette coach Buzz Williams said. "We had our hands full from the beginning."
Marquette was 17 for 21 from the free throw line, while Michigan was 12 for 18.
Michigan (3-1) got 22 points and nine rebounds from Manny Harris.
Harris had seven points as Michigan opened the second half with a 12-4 spurt to cut its deficit to 48-47. But Hayward scored six points and Butler added four in a 10-0 run by Marquette that made it 58-47 with 12 minutes to play.
"They're an excellent passing team, and low turnover numbers," Beilein said.
Hayward, who celebrated his 23rd birthday Thursday by scoring 27 points in Marquette's 71-61 victory against Xavier, gave the Golden Eagles a 70-57 lead on a putback with four minutes remaining.
"Hayward, obviously, is a great player," Beilein said.
Johnson-Odom had 12 of his points in the first half as Marquette took a 44-35 lead.
Michigan was just 3 for 20 from 3-point range.
"They did a great job of contesting shots," Wolverines forward DeShawn Sims said. "We just wasn't able to knock down any shots today. A credit to their defense; they did a great job defending us."
Hayward has 1,361 points, which moves him into 18th place on the Marquette career list.