Colin Castleton led Florida (15-9) with 19 points and 14 rebounds as the Gators battled back from a ten-point first half deficit. Scottie Lewis added 15 and Tre Mann had 14.
Nahiem Alleyne scored a career-high 28 points for Virginia Tech (15-7), including the game-tying three-pointer with less than two seconds to play that forced overtime. Tyrece Radford added 18 for the Hokies.
Florida rallies behind Castleton, Mann to move on
With the game at 10-8 in the early going, Virginia Tech went on a 11-3 run behind Hunter Canttoor nailed a trio of three-pointers in that stretch to give the Hokies their biggest lead of the game at 21-11 with nine minutes left. Virginia Tech would go on to take a six-point lead into halftime at 33-27.
Trailing 46-40 with just over 10 minutes to go, Castleton led Florida on a 16-6 run to give the Gators a 56-52 lead with four minutes remaining. Florida led by six when Locke fouled Allenye on a three-pointer and he made all of them to cut the lead in half.
Florida still led by three after two free throws by Lewis with 29.3 seconds remaining. Alleyne missed a three that would have tied the game, with Anthony Duruji grabbing the rebound and getting fouled with 7.3 seconds to go, but he missed both free throws.
Alleyne then nailed a hurried three-pointer with 1.7 seconds left to send the game into overtime. The two teams traded baskets to start the period, but then Castleton converted on a three-point play to give the Gators the lead. Two free throws by Radford were canceled out by two more from Castleton with 1:38 left to restore Florida's three-point advantage.
Cattoor scored on a layup after a Castelton turnover to make it a one-point game with 48 seconds to go. With the shot-clock winding down, Mann took a pass from Locke at the top of the key, worked his defender to right side of the arc, and bounced into a step-back three-pointer that put Florida up four with 22.9 seconds to go.
Virginia Tech misfired, Lewis made one of two free throws and Florida advanced to a second-round matchup with 15th seed Oral Roberts on Sunday.
Florida post-game quotes
Gators head coach Mike White described the up-and-down contest, saying "made it a little more interesting than we needed it to, [but] showed tremendous resilience to bounce back and find a way to win in overtime. If Colin doesn't step up like he does, we're going home.
"We stepped up defensively and got some stops. When you're getting stops, sometimes it flows into positive things offensively. This team continues to show character. No has been through what they've been through. Really proud of our guys."
Castleton, in having one of the best games of his career, said "we weren't losing the game. That's just what it comes down to. You've got to have the mindset of 'we're not losing this game'; we don't want to go back to Florida just yet.
"You just got to keep pushing, keep fighting."
Virginia Tech post-game quotes
Alleyne on his game-tying three: "I mean, it was a crazy feeling. It's everybody's dream to hit a big shot. Big-time players make big-time plays. But that wasn't really the play.
"We were supposed to give the ball to Tyrece, but they were shading his side. So, Keve [Aluma] passed it to me and I just knocked it down."
Head coach Mike Young was understandably disappointed after his team led pretty much the entire game.
"Hats off to coach White's Florida Gators team. Sometimes in this business, you think you know how things are going to play out in terms of pace on either end of the floor and that's not exactly what you're going to get.
"This was a really good Virginia Tech rebounding team, and Colin [Castleton] and [Anthony] Duruji and the rest of the Gators outrebounded us by a pretty good clip.
"And then we just couldn't get stops. We were up eight and miss a layup and they score. We were where we wanted to be and in good shape, and then we didn't handle some things very well.
"I thought Florida played well. They advance and we go back to Blacksburg, which is pretty hard to swallow."