A Stegeman Coliseum crowd of 7,982, which braved the season's first snow flurries to get the game, saw Georgia win its first SEC game while Alabama fell to 0-3 in the league.
The Bulldogs led by as many as 15 points in the second half but committed four straight turnovers late in the game to allow Alabama to close to within four at 55-51 with Mykal Riley hit two free throws with 1:42 remaining to cap an 8-0 Alabama run.
Georgia senior Billy Humphrey then made the biggest shot of the game, a rushed 3-pointer with the shot clock running out that put Georgia (10-5, 1-1 SEC) up 58-51 with 1:09 left and took the steam out of the Crimson Tide comeback.
"That pretty much iced it," head coach Dennis Felton said. "That turned it back into an easy win when it could have been otherwise."
It was 3-point shooting that saved the Bulldogs, and doomed Alabama, all night.
Georgia, which was coming off a game in which it hit less than 25 percent of its shots, was 10-of-22 from behind the 3-point line and shot 40.8 percent overall.
"We did bounce back as a team from the standpoint of being more patient and persistent to pass the ball and make extra plays to get better shots," Felton said. "We just simply made more extra passes. Many times today when we drove, we passed it."
Georgia lost 78-76 last year in Tuscaloosa, Ala., and felt like two officials' calls went against them in the final moments. The Bulldogs also blew a 15-point lead in that game, a memory which began to surface late Wednesday.
"We kept telling each other, stay poised, we've still got the game," said Humphrey, who was Georgia's leading scorer with 13 points. "We owed them one."
Nine of the 10 Bulldogs who played scored, and none reached double digits until freshman forward Jeremy Price hit two free throws with 4:19 remaining to give him 11 points.
Alabama junior Richard Hendrix had 19 points and grabbed 10 rebounds to help the Crimson Tide to a 35-28 rebounding advantage. v The Crimson Tide (11-7), which is off to its worst league start since 1999, shot a better percentage than Georgia overall but missed 17 of their 20 3-point attempts.
"We were playing hard, but we couldn't get anything going tonight," Alabama head coach Mark Gottfried said. "Our effort was there, but our execution and playing well was not."
Georgia hosts Arkansas at 7 p.m. Saturday.