Murray threw four touchdown passes to become the school's career leader, with the first three crucial in rallying the No. 13 Bulldogs for a 29-24 victory over Kentucky.
The junior finished 30 of 38 for 427 yards for Georgia (6-1, 4-1 SEC), which stayed within reach of East-leading Florida entering next week's showdown against the Gators (7-0, 6-0) in Jacksonville, Fla.
Georgia outgained Kentucky 504-329.
Kentucky senior Morgan Newton had a hand in all of the Wildcats' scores, running and passing for a touchdown and leading a field goal drive. He played the entire second half in place of freshman Jalen Whitlow, who left the game with a migraine.
Raymond Sanders ran for a 3-yard score for the Wildcats, Kentucky (1-7, 0-5) who lost their sixth in a row.
But the Bulldogs, coming off a bye following a 35-7 loss at South Carolina, had to work harder than expected. And the signs it would be a long night were apparent from the start.
Kentucky opened by driving 84 yards in 13 plays, mostly on the ground. Jonathan George rushed four times for 42 yards, Raymond Sanders added 13 and quarterback Jalen Whitlow 12 before Morgan Newton relieved him to complete the possession by finding Aaron Boyd for a 4-yard touchdown.
It ended a 20-game, first-quarter drought for the Wildcats, whose last first-quarter TD came Nov. 27, 2010 at Tennessee
Georgia gained just 20 yards on its first eight plays but tied the game by going 97 yards in just four.
After hitting Malcolm Mitchell for 14 yards and first down at the 34, Murray found a wide-open King for a 66-yard touchdown as the Bulldogs used just 1 minute, 37 seconds in completing its longest scoring drive this season.
Just as quickly, the Wildcats went back ahead with the help of an option pass that caught the Bulldogs off guard. On second and 9 from Georgia's 35, Whitlow threw left to Demarco Robinson before he threw it back across the field to Whitlow, who followed a wall of blockers for a 33-yard gain to the Bulldogs' 2.
Morgan's 2-yard run finished the 58-yard drive.
Murray and King connected again on Georgia's next possession, first for 48 yards to Kentucky's 5 and then for a 1-yard score two plays later to cap a 75-yard drive. Murray's 73rd TD gave him the school record, breaking David Greene's record set from 2001-04.
The moment was spoiled when Marshall Morgan missed wide right on the conversion, leaving the Bulldogs down by one. There was even more suspense to his 27-yard field goal that provided a 16-14 halftime lead, a kick that clanged off the left upright before bouncing through.
Then again, that drive had plenty of drama.
A wide-open Marlon Brown dropped Murray's deep pass. The quarterback fell to the ground for a sack and a 7-yard loss.
On third and 14 from Kentucky's 41, Gurley appeared to come up short of a first down before a generous spot that was upheld on review. Given 17 seconds to work with, Murray hit King for 19 yards to the 8, setting up Morgan's head-shaking moment.
Murray finished the half 15 for 19 for 243 yards.