Florida (22-9) held an 82-80 lead with 29 seconds left, but was unable to inbound the ball in time and was whistled for a five-second call.
The Bluejays set up for a last shot and Gators guard Justin Hamilton nearly forced a turnover when he stripped Ismael Caro. But the ball went out of bounds to Creighton with 4.5 seconds left.
With star player Kyle Korver having fouled out, Creighton went right to Taylor. The Missouri Valley Conference's Sixth Man of the Year dribbled twice and then hit his eighth three-pointer of the game over Florida's Brett Nelson.
"Coach designed the play for me to take it out, but switched it at the last moment to give me the ball," Taylor said. "I got a good look and took what came to me."
Two-tenths of a second were left after Taylor's shot and the Bluejays ran out onto the floor. Florida coach Billy Donovan complained afterward that a technical foul should have been assessed.
"Our guys were trying to inbound the ball," he said. "I told the official it was a technical foul."
Taylor's three-pointer with 35 seconds left in regulation capped a 10-2 run that created a 69-69 tie at the end of regulation.
Taylor matched his career high with 28 points as Creighton (23-8) snapped a three-game losing streak in the NCAA Tournament. The Bluejays are making their fourth straight appearance and survived Korver's absence.
"We were not prepared," Bluejays coach Dana Altman said. "Usually we bring Kyle off the top there and Terrell is the guy that comes off the baseline. So we had to flip-flop that around and we didn't have a timeout left to design anything else, so we went for the play."
Florida had chances to hold for the last possession at the end of regulation and the first overtime, but came up empty on both occasions.
Nelson, who injured his cheekbone in a fight in practice, badly missed a runner on the first opportunity and Justin Hamilton lost his dribble and had the ball stolen on the second.
The lack of execution down the stretch underscored a problem all year for the Gators, who finished 2-7 in games decided by five points or less.
Florida dismissed Teddy Dupay from the team before the season and Nelson, who went four of 19 from the floor, was unable to fully grasp the point guard position.
"They were the toughest first-round team we have had in the NCAA Tournament," Donovan said. "Terrell Taylor could play anywhere in America and Kyle Korver is one of my favorite players to watch."
Udonis Haslem led Florida with 20 points, including four in the second extra session. His two free throws with 1:36 left gave the Gators a 79-76 lead.
Michael Lindeman's layup cut the deficit to one, but Matt Bonner's three-point play provided a four-point cushion. Taylor had a layup to slice the lead in half before Florida's fateful failed inbounds attempt by Orien Greene.
Korver finished with 16 points and Mike Grimes added 10 for the Bluejays. Creighton will face Illinois in the second round.