Alex Tyus scored 19 points and grabbed 17 rebounds as Florida (29-7) beat BYU, 83-74, in overtime last night, chasing Jimmer Fredette and the Cougars (32-5) out of the NCAA Tournament. Florida reached its first regional final since 2007.

While Fredette was the star attraction, scoring 32 points on 11-for-29 shooting in the final game of his college career, Florida countered with balance.

Kenny Boynton added 17 points while Erving Walker and Chandler Parsons both scored 16. Boynton and Parsons each hit 3-pointers in overtime as Florida outscored BYU, 15-6.

But it was Tyus’s monster game that put the Gators over the top. The 6-foot-8-inch senior is the team’s fifth-leading scorer, averaging 8.6 points and 5.7 rebounds coming into the game.

“The thing about Alex is he never really gets fazed with the moment or with what’s going on,’’ Florida coach Billy Donovan said. “One of the things I’ve tried to pull out of him and get him to see is that when he has a lot of activity and he’s flying around the court, because of his athleticism, he’s got a great ability to impact a game.’’

While Tyus was battling under the basket, Boynton was glued to Fredette on defense.

Fredette made just 3 of 15 from 3-point range and had to work for his points against Florida’s physical defense. By the end of the game, he had a bandage on his chin from a blow in the second half, but the baskets kept coming until he was held scoreless in overtime.

When the outcome became apparent with one minute remaining, BYU coach Dave Rose subbed out Fredette, bringing a standing ovation from the crowd. He averaged nearly 33 points during three NCAA Tournament games, and finished the season by scoring at least 30 points in seven out of eight games.

Rose said Fredette’s legacy would be a simple one to define.

“Winning games — that’s his legacy,’’ Rose said. “He just helped his team find ways to win games.’’

The Gators led for much of the first half, but BYU rallied to tie the game at 36 by halftime.

Fredette, who came in as the nation’s leading scorer at 28.8 points per game, missed his first six shots. But the Cougars were able to tread water thanks to Jackson Emery and Stephen Rogers, who combined to hit five 3-pointers in the first half. Fredette was held scoreless for nearly 14 minutes before hitting a layup with 6:17 left in the first half. He made four of his next seven shots to finish the half with 10 points.

The Gators double-teamed Fredette occasionally, but usually guarded him with Boynton or Scottie Wilbekin. Fredette was bumped several times while trying to finish layups, and two of his first three shots were blocked. But fouls were hard to come by, despite Fredette’s occasional glares toward officials and the anger from the vastly pro-BYU crowd at New Orleans Arena.

“It was just a little frustration, just because that’s what happens sometimes during basketball games,’’ Fredette said. “But I tried to keep an even keel, and we were still right in there at the end of the game. We just didn’t win.’’

Parsons said he could tell Fredette was upset.

“That’s just a credit to our guys on defense — especially Kenny Boynton,’’ Parsons said. “He stayed with him and made it difficult for him out there.’’