The Yellow Jackets (14-10, 5-7 Atlantic Coast Conference) jumped to an early 17-2 lead and were ahead 50-40 at halftime, but couldn't put the game away in regulation.
Florida State's Adrian Crawford hit a running jumper in the lane with 4.5 seconds remaining in regulation to send the game into the first overtime tied at 91-91.
Little-used Florida State sophomore Ron Thompson and Jones each scored eight points for their teams in the first overtime that ended tied at 103.
Jones hit 10 of 12 shots, many of those dunks, and grabbed a game-high 17 rebounds while Collier added 10 rebounds.
Tony Akins added 18 points and Jason Floyd 16 for Georgia Tech, which hit 14 of 34 shots from 3-point range in the game.
Terrell Baker scored 26 points and Ron Hale added 24 for Florida State, which has now lost four straight ACC games. The Seminoles (12-11, 5-6 ACC) had claimed a 75-56 victory last month at Georgia Tech.
Thompson was pressed into action after four Seminole regulars had fouled out of the game. A fifth, Hale, fouled out in the second overtime.
Florida State took its first lead in the game at 75-73 with 6:55 left on a 3-point shot by Hale and the game see-sawed back and forth the rest of the way.