Senior Quantez Robertson blocks a three-point shot by Erving Walker at the end of the game.
The Tigers will play at 2:15 p.m. CDT in the semi-finals against a Tennessee team that Auburn beat in the regular season at Auburn.
Auburn coach Jeff Lebo called the victory over Florida a "grinder" that was won by his team's defense. Auburn held the Gators to 36.1 percent shooting, a season low for Billy Donovan's team.
Auburn managed to stay even at 37-37 on the boards with the taller Gators and blocked six shots, including the big one by Robertson, who said, "We won this game with our defense on a night when we weren't clicking all of the time on offense."
Auburn got 12 points apiece from Korvotney Barber and Frankie Sullivan and Barber added 10 rebounds for the Tigers.
Florida was led by 21 points from Alex Tyus. Gator star Nick Calathes was held to 3-13 shooting and finished with seven points.
"I think Auburn did a terrific job of getting up under him," Billy Donovan said of Calathes, adding Auburn's athleticism and tenacity with a major factor. "They made it very hard on him."
Both teams came out off-target with their shooting, but the Gators got on the scoreboard first taking a 5-0 lead before Tay Waller hit a tray at the 15:26 mark to score the first points for the Tigers.
"It feels pretty good to get a chance to play in the semi-final game and if we win that have a chance to play for the championship," Robertson said. "This means a lot to the seniors on the team--me, Vot, Rasheem and Drew (Smith). We wanted to be able to play for a championship and now we are two games away from making that happen.
"It is fun to be playing together as a team and doing the things we are doing right now," he added.
Freshman Frankie Sullivan said he was upset at himself for missing a free throw late in the game, but happy about the outcome, especially for the seniors.
"I think next time I am at the foul line I will make it," he said after just hitting the first of his two foul shots in the final minute.
Sullivan said Auburn's ninth win its last 10 games is due to teamwork. "Once you believe in your teammates you can do anything," he said.
The Tigers had several chances to take the lead in the closing minutes of the half, but didn't take advantage of the opportunities. However, at the break Auburn trailed only 29-28.
At halftime the Tigers were shooting 40.7 percent compared to 37.9 percent for Florida, which hit 11-29 field goals to Auburn's 11-27.
The Gators were 5-13 on threes compared to Auburn, which hit 2-10.
Florida held a 17-16 rebounding edge, but had eight turnovers, two more than the Tigers.
Sullivan was the big scorer for the Tigers in the first half with 11 while Barber and Waller scored four apiece. DeWayne Reed, Rasheem Barrett and Brendon Knox each had two points while Quantez Robertson played 11 minutes in the half without taking a shot.
Brendon Knox scores on a stuff for the Tigers on a fast break as a crowd announced at 14,128 fans watched the action at the St. Pete Times Forum.
Florida was led at halftime by Alex Tyus, who scored 12 points and added six rebounds.
Florida built the lead back to seven points early in the second half before Robertson scored on a layup and added a free throw as he was fouled at the 17:37 mark.
Auburn took its first lead of the game with 8:10 play on a three from the corner by Waller to put the Tigers up 44-43.
The Tigers built the lead to 51-46 at the 6:14 mark on a steal and fastbreak basket by Hargrove.
The game stayed close the rest of the way, but Auburn clung to its lead with good defense and timely shooting.
A dish from DeWayne Reed to Barber was slammed home by Barber to put the Tigers up 60-55 with 28 seconds left. That appeared to slam the door, but the Gators had other thoughts.
With 16 seconds left Walter Hodge hit a long three-pointer that got a kind bounce off the rim and went into the basket to cut the lead to 60-58.
Freshman Sullivan was fouled by the Gators with 13 seconds left. The guard hit his first shot, but came up short on the second.
With Auburn up by three, the Gators rushed the ball up court and Robertson blocked the final shot to preserve the victory.
Auburn improved to 22-10 overall with the victory.
On Auburn's side of the bracket in other quarter-final contest, Tennessee cruised past Alabama 86-62 in the first game of the night session. Tyler Smith led the Volunteers with 22 points in a game in which 10 UT players scored. Wayne Chism added 15 points while J.P. Prince posted a double-double with 14 points and 10 rebounds.
In the other afternoon contest Mississippi State delivered a blow to South Carolina's status as an NCAA Tournament team by knocking off the Gamecocks 82-68. Barry Stewart led Mississippi State in scoring with 21 points.
LSU will take on Mississippi State at noon CDT in the first semi-finals matchup on Saturday.
Junior Hargrove said the Tigers will have a major test on Saturday. "We have got to stay focused on defense and keep playing hard," he said. "Hopefully, some shots will fall for us."