Braxton Key had a career-high 24 points and helped Alabama (9-6, 2-1 Southeastern Conference) rally after trailing 34-16 with five minutes left in the first half.
Key had 12 points while the Crimson Tide closed the half on a 15-4 run, and Alabama took the lead on Donta Hall's tip-in about five minutes into the second half.
Stone hit a 3 to pull Florida (13-3, 4-0) within 53-50 with 10:50 left, then hit another to put the Gators ahead 61-59 with 6:49 remaining. Alabama didn't lead again.
Canyon Barry and Kasey Hill each had 13 points for the Gators, and Hill added five steals to help Florida get a 27-10 edge in points off turnovers.
Hall had 12 points and eight rebounds for Alabama.