Kentavious Caldwell-Pope finished with 25 points and Gerald Robinson had 19 for Georgia.
Ole Miss' Jarvis Summers made one of two free throws to give the Rebels a 10-point lead with 47 seconds remaining, but Henry and Summers showed why their school ranks last in SEC's free-throwing shooting, combining to miss their next four foul shots as Georgia twice cut the lead to two points in the final 23 seconds.
With 9 seconds left, Henry hit one free throw but missed the second attempt. Dustin Ware grabbed the rebound for Georgia and made a long pass to Robinson in the right corner, but Robinson's 3-point attempt bounced off the rim.
Nemanja Djurisic picked up the loose ball on the left side, but he launched a 3-point attempt that bounced off the rim and was pulled down by Henry at the buzzer.
Reginald Buckner, the SEC's leading rebounder in conference play, finished with six points and 10 boards.
Georgia never led after Robinson's jumper made it 8-7 early in the first half.
Ware went 0 for 7 beyond the arc and is now 6 for his last 31.
Demarco Cox's layup with 14:24 remaining gave Ole Miss its biggest lead at 14. The Rebels improved to 12-2 when leading at halftime.
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