Providence advanced the same way it stunned its way to a No. 1 seed in the Big East Tournament: just barely surviving, seemingly never running out of nails to bite.

The Friars rarely dominate opponents, but they also rarely lose to them.

Providence yet again flirted with a disastrous defeat, but the top-seeded Friars erased a three-point deficit in the last 80 seconds, riding a dominant center in Nate Watson and surprising late-game help to a thrilling 65-61 victory over No. 9 Butler in the Big East Tournament quarterfinals at the Garden on Thursday.

Providence (25-4) will meet fourth seeded Creighton, which outsed No. 5 Marquette 74-63, in the semifinals Friday at 6:30.

In front of an announced sell-out of 19,812 — largely Providence fans — in Midtown, the Friars stole the game with some defense from forward Justin Minaya and a 3 from senior guard Al Durham — who hadn’t knocked one down in more than a month.

The Friars were down a point in the final minute, when the ball kept moving around the perimeter until it found Durham, whose last triple was on Jan. 30. He erased an 0-for-18 skid and the deficit, giving the Friars a 61-59 bulge they would not relinquish.

“That’s a credit to my teammates, my coaches having faith in me,” said Durham, who shot just 20.9 percent from beyond the arc this season.

“You know what? He made it. And I trust him,” coach Ed Cooley said, his Friars finding yet another way to win. “He’s made some big shots for us the whole time. … I think today was a microcosm of the type of season that we’re having.”

On the ensuing possession, Butler’s Simas Lukosius thought he had a layup to tie it up — but Minaya, the son of former Mets GM Omar, emerged from behind to swat it away. After Bo Hodges missed a contested shot underneath, Providence, which hit its late foul shots, could exhale.

Minaya was quiet for much of the matinee and went 2-for-5 for six points, but he didn’t need his jump shot to save the Friars from ignominy. The four-point win was the narrowest margin for a No. 1 seed in the conference quarterfinals since 2012, when Syracuse beat UConn by three.

“I feel like he’s the best defender in the Big East,” Durham said of Minaya, a New Jersey native. “I feel he should be having national recognition about it.”

Providence won the Big East regular-season title — for the first time in program history — without a single member of the All-Big East first team. Tellingly, the Friars’ hardware included the top sixth man (Jared Bynum) and the conference’s coach of the year (Cooley), relying upon a well-coached and disciplined group to weather any obstacle it faced.

The formula worked again. Providence trailed by six with nine minutes to go, but panic never set in. The Friars pounded the ball underneath to Watson — 9 of 14 for a game-high 26 points — and chipped away until the lead evaporated.

No one on the balanced Providence team averaged more than 14 points, but Watson became the go-to option.

“Nate was a monster the whole night,” Cooley said. “We didn’t do a lot of things great, but we did enough to win.”

Providence lost four times this season but had an average margin of victory of just 5.9 points. The Friars — with a team-record five graduate students — relied upon their experience to guide them through late-game situations. They will gamble another day.

The Bulldogs (14-19), who probably should not even been playing in the game — they trailed by six with 45 seconds left against Xavier on Wednesday and found a way to advance — played a suffocating zone defense and got a huge second half from forward Bryce Golden, who scored all of his 13 points after the break.

But they went just 3 of 19 from 3, which doomed them.

“I don’t think there’s a better tournament in the world, let alone the country, than to play in the Big East Tournament right here in Madison Square Garden,” said Cooley, who will see at least one more day of the tournament.