The Gators broke open a close game to take a nine-point lead late in the contest, but Florida State rallied to tie it at 66-66 with 28 seconds to go on a pair of free throws by Ian Miller.
Scottie Wilbekin attempted a jumper for Florida with six seconds left and Finney-Smith rebounded his miss.
Finney-Smith was fouled and he made the second of his two attempts to put the Gators in front. A desperation 3-pointer by Miller at the buzzer failed to go for the Seminoles.
Florida (6-1) was led by 19 points from Casey Prather and 17 from Michael Frazier. The Seminoles, who slipped to 5-2, got 14 points from Boris Bojanovsky.