The Gators (13-2 overall, 2-0 SEC) gained possession after an offensive foul with 19.1 seconds remaning and Roberson calmly delivered his seventh three-pointer of the evening, capping a team-high 23-point effort.
It was the first home buzzer-beater for the Gators since 1993.
With a victory, the Gators ended the Bulldogs (9-4, 1-1) eight-game winning streak, while moving their own winning streak to nine.
Led by 10 first-half points by guard Ezra Williams, Georgia took a 35-30 lead into the locker room. The Bulldogs held the Gators to only 35 percent from the field and 16 percent from beyond the arc.
The Bulldogs stretched their lead to 10 with back-to-back layups by twins Jarvis and Jonas Hayes, followed by a three-pointer by Jarvis to put Georgia up 45-35 with 11:27 to play in the second half.
Senior forward Matt Bonner (Concord, N.H.) and Roberson led the Florida surge with 11:27 remaining, combining for 27 points in the final 11 minutes of play. After falling behind by 10 points, the Gators tore off a 23-4 run to take a 58-49 lead with just under five minutes remaining.
"I kept calling his [Bonner] number," head coach Billy Donovan said. "I forced him to step up and make plays for us."
Then began the Jarvis Hayes show.
Hayes scored nine straight points, hitting three straight treys to tie the game with 2:13 left.
Roberson hit his sixth three-pointer of the night, giving Florida a three-point lead. Rashad Wright hit a pair free throws and Hayes hit his fifth three-pointer of the half to give Georgia a two point lead with less than a minute in the game.
Senior Justin Hamilton (Sarasota, Fla.) dished the ball to an open Roberson who nailed the three-point shot as the clock expired, giving Florida the decision in front of a school SEC home-opening record 12,422 fans.
Florida is now 13-2, including 2-0 in the SEC, and will face Tennessee on Wednesday night at the O'Dome. The game tips off at 7 p.m. and will be broadcast on the Sunshine Network on a tape-delayed basis to most of the state.