MINNEAPOLIS — By grit, by luck, by any basketball means necessary, Virginia lives. The Cavaliers cannot die, it seems. They will not die. After years of collecting despair in the NCAA men’s basketball tournament, they have been granted a spring full of grace. Drama, too. But mostly grace.

For the first time in team history, they will play for the national title Monday night, and for that, they should thank the doughty referee who called a controversial last-second foul on Samir Doughty. They should thank the unshakable Kyle Guy, their latest unforgettable clutch savior, who stepped to the line and made the three biggest free throws of his life to nip Auburn, 63-62, on Saturday night at U.S. Bank Stadium.

And they should thank the Tigers and their coach, Bruce Pearl, who has been called a scoundrel for his rule-violating sins but who handled the gut-wrenching defeat with so much class that it makes it much easier for Virginia to move forward without an overwhelming amount of defensiveness.

Just a week ago, the Cavaliers advanced to the Final Four via one of the greatest games in tournament history, an 80-75 overtime classic against Purdue. Mamadi Diakite was their legend on that night for tossing in an improbable buzzer-beater to complete an improbable three-point possession that forced overtime. Now there’s Saturday’s wild finish to commit to memory. And there’s another tournament hero to embrace for eternity. Diakite will gladly make room for Guy.

“Mine is still lasting,” Diakite said, smiling in the locker room. “He’s got the title of the most incredible free throws ever. It wasn’t a shot, though, like mine.”

While this game wasn’t as well played as the Elite Eight shot-making marathon, the ending will be talked about for decades. The game seemed over when Virginia pulled ahead 57-47 with a little more than five minutes remaining. Then it seemed the Cavaliers had fallen apart during a 14-0 Auburn run that featured the incredible shooting of the streaky Bryce Brown. The Cavaliers trailed 61-57 with 17 seconds left, but Guy drilled a three-pointer to trim the deficit to one point. After Auburn guard Jared Harper made one of two free throws with seven seconds remaining, the game was set up for its crazy ending.

Virginia ran a play it likes to refer to as “Kyle Get Open.” Ty Jerome — who seconds earlier appeared to dodge a double-dribble call before he was fouled — found Guy open for a corner three-point attempt. He jumped in the air and leaned as he shot the ball. Doughty defended him almost perfectly, it seemed. But official James Breeding “ruled that Doughty moved into the airborne shooter, making contact with Guy while taking away his landing spot,” according to a postgame statement by J.D. Collins, the NCAA national coordinator of officiating.

It was subtle. But it happened. And with the game on the line — a game that featured so few fouls until the end that both teams were scrambling to use the fouls they had to give before they were in the penalty — Breeding called it. Was he right? By the letter of the law, yes. But we’re also used to officials swallowing their whistles during such situations and letting the players decide the game.

The decision was complicated. It was right; Virginia has no reason to apologize for outlasting a third straight opponent in this tournament. It was wrong; how can anyone stomach Auburn losing like that?

“I do feel for Auburn,” Virginia Coach Tony Bennett admitted afterward. “But I feel better for us.”

It would have been just as difficult for the Cavaliers to handle losing, especially after building that 10-point lead and closing with uncharacteristic sloppiness and mental lapses. Before Brown got hot and the Cavaliers panicked, they had fought off an opponent that just wouldn’t go away.

The freewheeling, three-point-shooting Tigers were predictably forced to play at Virginia’s pace from the beginning. They were okay with that, however. There’s much more to Auburn than playing fast and hoisting jumpers. They have proved that over the past month, winning 12 straight games, capturing the SEC tournament title and running through the Midwest Region of this tournament by defeating superpowers Kansas, North Carolina and Kentucky.

Sometimes the Cavaliers paralyze opponents unfamiliar with them when they lull foes into a nuanced style that requires more efficiency, patience and determination than they can stand. Auburn wasn’t afraid of the grind, and despite its oversimplified reputation of preferring to be flashy, there had been ample evidence in its 39-game journey to Minneapolis that the Tigers actually win with chameleon traits. They’re down for whatever the game requires. They’re a tough team to fluster.

Auburn missed 11 of its first 14 three-point attempts, but it led 31-28 at halftime. The Tigers found a way to be comfortable in an uncomfortable game, crashing the offensive glass and outrebounding the bigger Cavaliers. They utilized their depth; Bruce Pearl gave time to nine players in the first half. The Tigers played four reserves a total of 35 minutes before halftime. Virginia’s two subs, Jack Salt and Braxton Key, were on the court for a combined 9½ minutes. They just kept attacking. Normally, when you play Virginia’s game, it has to be orderly and methodical. For Auburn, there was still havoc and flurries of unconventional genius within the structure.

“They’re great,” said Diakite, who scored only two points but blocked five shots and grabbed six rebounds. “There’s no one way to describe them. They’re physical. They’re athletic. They’re fiery and competitive, but they’re cool. They don’t seem to be what people think of them, as far as how cocky you think they play. Hats off to them. We’ll always respect them.”

To get past Auburn, the Cavaliers needed 21 points, nine rebounds and six assists from Jerome, who played a terrific floor game before he got in foul trouble late. Guy scored 15, and De’Andre Hunter shook off a poor first half and attacked the basket in the second half. He scored 10 of his 14 points after halftime.

Still, they had to take back this game after Auburn stole it in the closing minutes. It was so close to being over that Pearl, who didn’t hear controversial foul call at first, was walking to shake Bennett’s hand before realizing what had happened.

“WHAT?!?!?!” he exclaimed.

He stomped back to the sideline before composing himself. Then Guy made the free throws and turned a valiant Auburn performance into a nightmare.

“These are the moments that every basketball player has dreamed of,” Guy said. “Kind of had that feeling in your stomach, like a good nervousness.”

Somehow, Auburn managed the perspective not to focus too much on the ending.

“I can’t question none of that,” Doughty said.

Said Pearl: “My advice, as an administrator of the game, is if that’s a foul, call it. Call it at the beginning of the game. Call it in the middle of the game. Call it at the end of the game. Don’t call it any more or less at any other time during the game. That was the call.”

He went on to praise Jerome and his players for nearly pulling off an incredible comeback.

“I’d love for that to be the story,” Pearl said.

For many, it won’t be that easy. We all love to debate questionable endings. But Auburn refused to deny Virginia. And the Cavaliers aren’t going home just because the ending was a little messy.

No, they’re going to play for the championship. And you get the feeling this tournament, this entire season, is destined to break their way.