San Diego State guard Lamont Butler celebrates with teammates after hitting the winning basket against Florida Atlantic in a Final Four game Saturday in Houston. Godofredo A. Vasquez/Associated Press

HOUSTON — San Diego State’s vaunted defense staggered well into the second half as free-flowing Florida Atlantic breezed to a 14-point lead.

The Aztecs found their teeth again to get back into the game. Then Lamont Butler delivered at the very end.

Butler hit a buzzer-beating jumper for the ages, sending San Diego State to its first national championship game with a 72-71 win over fellow mid-major Florida Atlantic in the Final Four on Saturday night.

“I didn’t really know how big it was,” Butler said after his calm reaction to one of the greatest shots in NCAA Tournament history. “We’re going to the national championship. That’s not things many people do.”

A diabolical defense had pushed San Diego State (32-6) all the way to the final stop for the NCAA tourney. The Aztecs bumped and harassed opponents all season to create the first all-mid-major national semifinal since VCU and Butler in 2011.

The swaggy Owls (35-4) seemed to have solved San Diego State’s vaunted defense, using constant movement and ball reversals to create mismatches they could exploit.

San Diego State found its defensive mojo midway through the second half, clamping down on the Owls while whittling their lead down to one on Jaedon LeDee’s short jumper with 36 seconds left.

When FAU’s Johnell Davis missed a contested layup, San Diego State Coach Brian Dutcher opted to not call timeout, joking that he didn’t have any plays left.

All the Aztecs had to do was get the ball to Butler.

With the clock ticking down, Butler dribbled to the baseline, found that cut off and circled back. He stepped back to create a little room and hit a jumper that sent the Aztecs racing out onto the floor and had San Diego Padres fans going wild at Petco Park.

“The plan was just to get downhill,” Butler said. “They cut me off a little bit. I looked up, there was two seconds left, so I got to a shot that I’m comfortable with. And I hit it.”

Next up for the Mountain West Conference’s first Final Four team is a matchup Monday night against UConn.

“We’ve always been knocked down,” said San Diego State’s Matt Bradley, who had 21 points after struggling in the previous three games. “But the biggest thing we always do is get back up and keep fighting.”

The Owls led 40-33 at halftime after hitting 5 of 11 from 3-point range against a defense that held its previous two NCAA Tournament opponents to 5-of-44 shooting from the arc.

FAU kept making shots, stretching the lead to 14 midway through the second half.

Then the Aztecs got gritty.

Contesting nearly every shot and pass while pulling down a string of offensive rebounds, including six in 59 seconds, San Diego State rallied to tie it at 65-all.

“They went on a run, getting extra possessions,” said FAU’s Nick Boyd, who hit three early 3s and finished with 12 points. “That was really the turning point of the game.”

FAU kept San Diego State at bay most of the second half thanks to Alijah Martin, who seemed to have an answer for every Aztecs move by scoring 19 of his 26 points in the second half.

He hit a reverse layup with 45 seconds left to put FAU up 71-68, but it wasn’t enough to prevent the Owls’ improbable run from coming to an end.

“These guys have created memories and a legacy that will last a lifetime,” FAU Coach Dusty May.

UCONN 72, MIAMI 59: UConn doled out another drama-free basketball beatdown, getting 21 points and 10 rebounds from Adama Sanogo to dispatch Miami and move one win from the school’s fifth national title.

Jordan Hawkins overcame his stomach bug and scored 13 for the Huskies, who came into this most unexpected Final Four as the only team with any experience on college basketball’s final weekend, and with the best seeding of the four teams in Houston – at No. 4.

Against fifth-seeded Miami, they were the best team on the court from beginning to end. Starting with three straight 3s – one jumper from Hawkins and two set shots from Sanogo – UConn took a quick 9-0 lead and never trailed.

The game was more of the same from the Huskies (30-8). The double-digit victory over Miami was UConn’s closest win in five tournament games.

Isaiah Wong led the Hurricanes with 15 points on 4-for-10 shooting. Harassed constantly by Sanogo, 7-foot-2 Donovan Clingan and the rest of Connecticut’s long-armed, rangy perimeter players, Miami, which entered with the nation’s fifth-best offense, shot 25% in the first half and 33.3% for the game.