LOUISVILLE, Ky. —  The program that 25 years ago was among the worst in college basketball, that had 14 losing seasons in 15 years, that had never been ranked in the Associated Press poll until 2010, that hadn’t won an NCAA Tournament game until 2011, that hadn’t been past the Sweet 16 until Friday, that doesn’t play in a power conference, that crams into middle seats on Southwest Airlines for road trips, that has two players in its rotation who had no Division I scholarship offers out of high school — is going to the Final Four in Houston.

Take a breath and think about it.

There are 363 men’s college basketball teams in Division I. Four will play in Houston for the national championship. And San Diego State is one of them after beating Creighton 57-56 in the South Region final on Sunday at Louisville’s KFC Yum! Center.

The San Diego State Aztecs.

The school that won one Division I national title, in men’s volleyball in 1973 — and dropped the sport.

But it will play for another, starting Saturday in the semifinals against Cinderella Florida Atlantic. Connecticut is in the other semi against either Texas or Miami.

It will because Darrion Trammell made a free throw with 1.2 seconds left after drawing a foul on Ryan Nembhard while attempting a game-winning floater — a whistle that Creighton fans, no doubt, will rue for years.

The Aztecs had the ball and a 56-54 lead with 33.7 seconds left and a sideline inbounds. Adam Seiko already had called a timeout because he couldn’t find someone open. The next time, he threw a lob to Micah Parrish that Creighton’s Baylor Scheierman intercepted under the Bluejays basket and laid in.

The Aztecs ran down the clock and had a midcourt inbounds with 6.7 seconds left. The original play wasn’t open and Lamont Butler inbounded to Aguek Arop, who handed off to Darrion Trammell, who dribbled off a ball screen and lofted a floater from just inside the free throw line with Nembhard on his back.

The shot bounced off the front rim.

Whistle.

Anecdotally, officials across the country have been swallowing their whistles in the final seconds. But official Lee Cassell didn’t, and soon Trammell was at the line for two shots.

Miss.

Make.

Buzzer.

History.

That ended a harrowing second half, with the Aztecs trailing, taking the lead, falling behind again and then leading again. Over the final seven minutes, the game was tied six times.

Lamont Butler led the Aztecs with 18 points. Trammell had 12. Nathan Mensah had eight, including a clutch jumper with 1:35 that put them up 56-54 after Creighton had drawn even on a pair of baskets by 7-foot-1 Ryan Kalkbrenner (17 points).

The Aztecs shot just 37.7%, below Creighton’s 40 percent, but they compensated with 13 offensive rebounds that they converted into 13 second-chance points. They also held the Bluejays to 2 of 17 behind the 3-point arc.

The Aztecs coaches said Creighton would be a different beast for their increasingly impermeable defense, and it was. The problem is that all five players on the floor can score in multiple ways. Add to that maybe the nation’s best little-big combination in Nembhard and Kalkbrenner working off high ball screens.

Five times in the first half alone, the Bluejays drove the paint to stress the defense and then flipped up lobs to the rolling Kalkbrenner. That didn’t include a play where Nembhard drove, had a bad angle but shot it anyway — almost intentionally missing to the far side of the basket — because he knew Kalkbrenner would clean it up, which he did.

But all things considered, despite their defensive struggles, the Aztecs couldn’t be completely displeased entering the halftime locker room down only 33-28. The Bluejays shot 53.8% against a team that had been allowing 32.2% during the tournament and Kalkbrenner already had 10 points. The Aztecs didn’t have an offensive rebound until two minutes left in the half and had surrendered 20 points in the paint.

Creighton led by as many as eight before an 8-0 Aztecs run tied it with 2:44 to go in the half. But they missed their next six shots while Baylor Scheierman hit a floater in the lane and Nembhard drained a 3.

The Aztecs regrouped at intermission and responded by scoring the first six points of the second half to take their first lead since 5-4. They finally figured out how to stop the Bluejays, which opened the half 4 of 21 overall and 0 of 8 behind the arc. The problem, though, was scoring themselves.

The Bluejays capitalized on a five-minute, 0 of 10 shooting drought to move ahead 41-34. The Aztecs got back-to-back baskets from Butler but then went another five minutes without a basket.

But then Keshad Johnson made a tough, contest hook shot in the lane, was fouled and drained the free throws. Then Trammell scored on the break. Then an offensive rebound and follow by Johnson. Then a pull-up by Butler. Then two hoops inside from Arop.

The team with separate five-minute droughts without a basket suddenly had scored on six straight possessions. The Final Four, suddenly, was in reach.