DETROIT — Without Isaac Haas, Purdue played fine for the most part.

Until the last few minutes, when the Boilermakers’ season nearly slipped away.

“We lost our poise there, but then we also regained it,” coach Matt Painter said. “And Dakota Mathias made a huge shot.”

Mathias sank a 3-pointer with 14.2 seconds left, and second-seeded Purdue held off 10th-seeded Butler 76-73 on Sunday to reach the Sweet 16 for the second consecutive year. Haas, the 7-foot-2 center who broke his elbow in Friday’s win over Cal State Fullerton, did not play, but the Boilermakers prevailed anyway despite a late push by their in-state rivals.

Purdue (30-6) led by as many as 10 points in the second half, but Butler (21-14) cut the deficit to two and had the ball in the final minute. Kelan Martin missed a 3-pointer, and the Boilermakers were able to settle down.

“We can still win the game with that one possession, and we were able to do that,” Painter said.

The shot by Mathias made it 76-71.

“Once it left my hand it felt pretty good,” Mathias said. “Those last couple of minutes we kind of got out of our element, forcing some things offensively, not making the right read, to let them back in. ... Give Butler a lot of credit. They played hard. They’re a good team. We’re excited to come out with a win.”

Martin scored with 2.1 seconds remaining, and P.J. Thompson missed the front end of a one-and-one, giving Butler another chance. The Bulldogs called a timeout with 1.8 seconds left, and Kamar Baldwin’s shot from near midcourt hit the rim — although it may have been waved off on a review even if it had gone in.

Vincent Edwards scored 20 points despite early foul trouble for Purdue, and Matt Haarms filled in capably for the injured Haas. The Boilermakers set a school record for victories in a season and are in the regional semifinals for the fourth time under Painter. Purdue faces third-seeded Texas Tech on Friday in Boston.

Martin scored 29 points for Butler.

“Every day at practice, this group, they came and they embraced and they were willing to learn,” Butler coach LaVall Jordan said. “So I just wish we could have done better, so we could still coach them for a few more practices and at least one more game.”

Haas warmed up before the game but wasn’t using his injured arm much, and an official said a few minutes before tipoff that the big man’s brace hadn’t been approved for competition. Haarms, a redshirt freshman, started for the first time this season and missed an easy layup early on.

But the 7-foot-3 Haarms settled in, finishing with seven points and six rebounds. He was on the court at the end, using his huge frame to guard the inbound passer on Butler’s last play.

“This is for Isaac,” Haarms said. “This one’s for him. He helped me a lot today, but he has always been like that. He’s always in my ear and a great mentor.”

Haas was ruled out for the rest of the tournament after his injury Friday, but on Saturday, there appeared to be at least some possibility he could come back. He didn’t on Sunday, and he was noncommittal afterward about the next couple of weeks.

“We’ll see,” Haas said. “It just depends on how the inflammation goes down and if we can find a brace that meets NCAA regulations.”