Kentucky's Austin MacGinnis, who hit a 51-yarder to tie the game late in the fourth quarter, missed a 41-yarder to start the third extra frame.
Jones had consecutive big runs that put Florida at the 1 and then slammed through the line on second down for the game-winner.
The play of the game was Florida's fourth-and-7 conversion in the first overtime. Jeff Driskel floated a ball to the back corner of the end zone and found Demarcus Robinson for a 9-yard score.
Robinson finished with 15 receptions for 216 yards and two scores. He tied Carlos Alvarez's school record for catches in a single game.
