The first-place Gators (14-5, 6-1 Southeastern Conference) saw their 45-37 second-half lead become a 56-53 deficit before they regrouped behind Chiozza's 3-pointer, Hayes' jumper and Stone's layup to go ahead 62-58 with 2:02 remaining. KeVaughn Allen added two free throws with 44 seconds left before Hudson made two more from the line, shots that offset 3-pointers by Kevin Knox and Wenyen Gabriel.
Stone's missed free throw gave Kentucky a chance to tie at the end, but Florida denied drives by Quade Green and PJ Washington before stealing the inbounds pass with 2.5 seconds left to win for eighth time in nine tries and take a two-game SEC lead on the Wildcats (14-5, 4-3).
Stone finished with 14 points, Chiozza scored 13 with eight assists and Allen had 11 as Florida won despite shooting 33 percent (22 of 66).
Shai Gilgeous-Alexander and Wenyen Gabriel had 10 points each for Kentucky, which lost its second in a row and third of five.