The Dayton band director had changed into a sequined jacket, shimmering red and blue beneath the FedEx Forum lights. The Flyers’ players, 11 of whom had scored here Thursday night and left their opponent exhausted, were hugging one another and pointing to the rafters. “We are U-D,” the crowd roared, as if the college basketball world still needed to learn the identity of the NCAA tournament’s latest Cinderella.

In the biggest moments of Dayton’s improbable season, Coach Archie Miller has resisted the natural urge to trim his rotation, and it was the impeccable ability to muffle every threat that sent No. 11 Dayton into Saturday’s South Region final with an 82-72 victory over No. 10 Stanford.

“When the games are bigger, when the moments are bigger, you get with the guys who have been there the longest,” Miller said after the game, in which his bench had outscored Stanford’s by 32 points . “But at the end of the day, this team isn’t built that way. They’re that way every day in practice, so you’ve got to give them that chance.”

Few gave the Flyers (26-10) any sort of chance when the 2014 NCAA tournament bracket was released, and yet here they stand, one victory from their first Final Four since 1967, armed with a phalanx of contributors.

Against Stanford, leading scorer Jordan Sibert had 18 points, starters Devin Oliver and Matt Kavanaugh combined for 22 and reserve freshman Kendall Pollard, who has logged single-digit minutes in 23 games this season, managed 12 points Thursday.

This game felt entirely different from the checkpoints Dayton encountered to get here.

The Flyers withstood last-second misses by No. 6 Ohio State and No. 3 Syracuse to emerge from the first weekend as the tournament’s underdog story.

Asked Thursday night about coasting to a victory in which the Flyers handed out 19 assists against nine turnovers, Sibert cleared his throat behind the microphone.

Next to him, Pollard began to smile.

“It was definitely a relief,” Sibert said. “It’s nerve-wracking when you have to make that stop or get a game-winning shot to get the win.”

Instead, Dayton took advantage of a Stanford interior burdened by foul trouble and a poor shooting night from leading scorer Chasson Randle (21 points on 5-for-21 shooting ).

A technical foul on Cardinal Coach Johnny Dawkins did little to spark his team. When center Stefan Nastic fouled out late in the second half, taking with him 15 points of pure inside muscle, he gathered his teammates around and screamed at them, “Let’s go.”

The applause from the Flyers faithful grew even louder and threatened to drown him out.

“It was a home game,” Miller said later of the decidedly Dayton-leaning crowd.

His players took care of the rest, busting Stanford’s zone with eight three-pointers. By halftime, Dayton was ahead 42-32 by simple virtue of outworking its opponent.

One extra pass became an open shot. Missed attempts, which Stanford (23-13) sometimes allowed to clang off the rim and bounce around untouched, were scooped up and converted.

At times, Stanford was so overcommitted in its defense that the backside three-pointer became a treasure trove for the Flyers, mined over and over again.

It was exactly the scenario Miller had envisioned during his rapid ascension into the national spotlight, moving from beneath the shadow of his brother Sean, the head coach at Arizona, thanks to the bodies he has stuck with all season long.

By the time Dawkins emptied his bench, affording his seniors one last ovation amid the Dayton din, it was too late to catch up.

“They were relentless,” Dawkins said of the Flyers. “That’s the best way I can put it. They came in waves.”