"This is what happens when you believe," Rice said. "This is what happens when you don't think the impossible is impossible. This is what happens when you follow the formula, when you play for one another. (We) had the will and the determination."
Carter showed tremendous leadership and made the tough shots. He finished 12 of 24 from the field, and 2 of 5 on 3-pointers, hitting from long range to tie it with 18 seconds left in the first overtime.
"My teammates had confidence in me," Carter said. "I took the big shot and made it."
The Scarlet Knights (8-5) also came back from a seven-point deficit late in regulation in posting their biggest win since knocking off No. 9 Villanova at home last season.
"He reminds me of Bernard King," fellow freshman Jerome Seagears said of Carter. "He could have had 62 or 63 tonight if he was open."
Erving Walker had a chance to tie the game for the Gators (11-2) in the final seconds, but his off-balance attempt from the foul line hit off the rim.
Scarlet Knights fans stormed the court to celebrate in a game billed as the return of former Rutgers star and current Gator Mike Rosario to Piscataway.
"I thought the difference in the game, in my opinion, was I thought their guys played the right way," said Florida coach Billy Donovan, who felt his team got off to a good start and then showed only brief flashes after that.
Kenny Boynton matched his season high with 26 points for Florida. Bradley Beal added 15 and Erik Murphy had 14 points and eight rebounds for Florida, which was playing its first game at the loud and intimidating Rutgers Athletic Center.
"They wanted it more than us," Boynton said. "We made too many mistakes. It wasn't the underclassmen. It was the upperclassmen. That's disappointing. I take full responsibility."
Carter, whose previous high was 21 points, put the Scarlet Knights ahead for good at 80-78 with a shot in the lane. He was fouled on the play but missed the free throw.
After Beal missed a drive on the left side and Boynton missed a 3-point attempt, Carter scored inside again for an 82-78 edge.
Beal cut the Gators' deficit to a point on a 3-pointer with 1:18 to go, but Mack came right back with a 3-pointer with 55 seconds left for an 85-81 lead.
A floater by Walker with 44.8 seconds left cut the margin to a basket and Florida got a final shot when Rutgers was called for a shot clock violation with 8.7 seconds left.
Rutgers knocked the ball out of bounds in the backcourt with 4.3 seconds left and Walker could not connect after taking the inbound pass and driving to the foul line for his final shot.
Rutgers forced the first overtime by rallying from a seven-point deficit in the final 2:48 of regulation and the came from three points down in the first overtime with Carter tying the game at 76 with a 3-pointer with 18.2 seconds to play.
Florida turned the ball over in the waning seconds and Mack's 40-footer at the buzzer wasn't close.
The Scarlet Knights trailed 64-57 late in regulation before scoring the final seven points, aided by two Gators turnovers. Mack started the comeback with a 3-pointer, Carter scored in the lane and Miller tied the game with 45.7 seconds to go with a layup.
After Walker's drive down the lane with about 15 seconds left hit nothing, the Scarlet Knights blew a chance to win. Mack seemed to lose track of time and his off-balance shot never had a chance.
Florida had seemingly taken command when Boynton scored on a fast break after Murphy blocked a shot with Rutgers up 55-54. Then Boynton came back on the next possession to hit a 3-pointer for a 59-55 lead. The lead eventually grew to 64-57 on a three-point play by Boynton with 2:48 to play.
Rosario averaged 16.4 points in his first two seasons with the Scarlet Knights before transferring to Florida. He sat out last season and has been coming off the bench for the Gators. He scored five points in 14 minutes in his return and he was booed every time he touched the ball or cheered every time he missed a shot.
During warmups there were chants of "Rosario is a bum" and "Jersey hates you."
The only other cheers he got were when he missed a shot or when he was called along with Miller for a double technical foul with 54.7 second left in the half.