GAINESVILLE, Fla. -- The only thing No. 15 Florida did really well Friday night was chase loose balls.

It ended up being the key to another victory over rival Florida State.

Dorian Finney-Smith, who was fouled after grabbing the team's 20th offensive rebound, made a free throw with 1.3 seconds left that lifted the Gators to a 67-66 victory against the Seminoles.

"Give our guys credit for chasing it," coach Billy Donovan said.

Finney-Smith deserved the bulk of the praise. The sophomore struggled all night from the field, missing 10 of 12 shots, but came up big in the clutch. And on the glass. He finished with six points and 10 rebounds, including six on the offensive glass.

His last one proved to be the difference in an ugly game that included nearly as many fouls (38) as baskets (45).

Finney-Smith grabbed an offensive rebound on a missed jumper by Scottie Wilbekin and got fouled on the putback. He missed the first free throw, but gathered himself and sank the second for the Gators (6-1).

"I just went up there like every day in practice and shot with confidence," Finney-Smith.

His confidence seemed shaky earlier in the game. Donovan pulled Finney-Smith after he missed a third dunk, upset about his body language.

"I was like, `Move on right now. You're draining energy from me. I'm having a hard time trying to get excited coaching watching you walk off the floor right now," Donovan said. "But to his credit, he did try to move past."

Florida State (5-2) had a shot to win it, but Ian Miller's desperation heave from half court bounced off the back of the rim, missing by inches.

"I was proud of the fact that we fought," FSU coach Leonard Hamilton said. "We hung in there and gave tremendous effort, but unfortunately coming close doesn't count."

Miller finished with 13 points and Boris Bojanovsky had 14 points for Florida State. Aaron Thomas added 12 points and Michael Ojo had 10 for the visitors.

Casey Prather led Florida with 19 points, and Michael Frazier II added 17.

The Gators extended their home-winning streak to 20 and won their fifth straight in the series.

The latest was a nail-biter.

Frazier's fifth 3-pointer put Florida up 63-55 with 3 minutes to play. It was the largest lead of the game for either team, but it didn't last.

The Seminoles made eight consecutive free throws, trimming the deficit with the clock stopped.

Wilbekin also helped Florida State get back in the game. Playing in his second game back since a suspension, Wilbekin missed two free throws with 2:18 to play and had a careless turnover on the next possession.

Miller's 3-pointer cut Florida's lead to 65-64 with 1:10 to play.

Bojanovsky's block on Will Yeguete was also key. Bojanovsky, however, fouled out on Florida's next possession. Prather made one of his two free throws, but Miller tied it with a pair from the charity stripe with 28.3 seconds to play.

Donovan called timeout and drew up a play for Wilbekin. The senior dribbled near midcourt until the clock hit 10 seconds and drove to the elbow. His jumper missed wide, but Finney-Smith was in perfect position for the offensive board.

"We allowed them to get the rebound in the last few seconds," Bojanovsky said.

Still, the Seminoles watched Miller's shot nearly fall.

"If it goes in, you've got to live with it," Donovan said. "The worst thing you want to do in that situation is foul or have him throw the ball all the way into the lane and get sealed off and give up a layup. He almost made a heck of a shot. You've got to give the kid credit for at least giving the ball a chance to go in."

The Gators shot 38.3 percent from the field, missed 10 of 16 shots from beyond the arc and finished 15 of 24 from the free-throw line. But they made up with those offensive boards.

"I thought that was the difference in the game," Donovan said.