Kentucky (16-5, 4-4 Southeastern Conference) began the game with the nation's fifth-highest scoring average, but the Wildcats placed just one player — Samarie Walker with 10 points — in double figures.
Krista Donald finished with 10 points and Shacobia Barbee had nine points and 10 rebounds for Georgia (15-6, 3-5 SEC).
With 22 seconds remaining, Marjorie Butler hit one free throw to give the Lady Bulldogs a 58-56 lead, but missed the second, and DeNisha Stallworth grabbed the rebound for Kentucky.
But Krista Donald stole the ball from Jennifer O'Neill as the Wildcats point guard was driving the baseline with 10 seconds left.
After Georgia's Tiara Griffin missed a free throw, O'Neill missed a 3-point attempt at the buzzer.
Krista Donald, whose layup ended a 13-2 run that put the Lady Bulldogs up 42-37, hit an 18-footer that made it 48-42 with 8:23 remaining.
Kentucky, which began the game with five players averaging double figures, needed until the 4:36 mark of the second half before Walker hit a pair of free throws.
The Wildcats' last seven SEC games have been decided by 11 points or less. They are 3-4 in that stretch.
Kentucky was trying to win consecutive road games against Georgia for the first time in school history
The Lady Bulldogs, who missed 28 of their first 36 shots, took a 36-35 lead on Griffin's layup with 12:36 remaining.
Georgia began the season 11-0, but started 0-4 in the SEC for the first time in school history.
The Lady Bulldogs improved to 17-4 in Athens against Kentucky.