Murray completed 30-of-38 passes while breaking the Bulldogs' career TD pass record, surpassing David Greene's standard of 72.
Tavarres King scored twice, hauling down nine passes for 188 yards as Georgia (6-1, 4-1 SEC) rebounded from a loss to South Carolina following a bye week.
The Bulldogs' next game will be against Florida (6-0 in the SEC) for control of the conference's East division.
Jonathan George led Kentucky (1-7, 0-5 SEC) with 87 rushing yards on 12 carries.
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