Murray overcame an early interception in the end zone, hooking up with freshman Reggie Davis on a 98-yard TD - the longest pass play in school history. Arthur Lynch and Chris Conley also had touchdown catches for the Bulldogs (2-1).
The Mean Green (2-2) came in as a 33-point underdog, but big plays on special teams helped make a game of it. Brelan Chancellor returned a kickoff 99 yards for a touchdown, and Zac Whitfield fell on a blocked punt in the end zone early in the second half to stunningly tie the game at 21.
Murray made sure the Bulldogs avoided the upset. He scored on a 1-yard sneak and went to Conley on a 4-yard TD.
Murray became only the second Southeastern Conference quarterback with 100 career scoring passes. The three TDs pushed his total to 102, trailing only 1996 Heisman Trophy winner Danny Wuerffel of Florida (114).
Darnell Smith had North Texas' only non-special teams score, hauling in a 20-yard pass from Derek Thompson. But the Mean Green certainly didn't embarrass themselves on a rainy day between the hedges, collecting a hefty payout ($975,000) and ruining any hopes Georgia had to limit the playing time of its starters before an SEC showdown with No. 6 LSU next weekend.
Murray got off to a rough start, trying to force a pass into heavy coverage on second-and-goal from the North Texas 3. It was picked off by linebacker Will Wright.
Murray bounced back on the next possession. He hooked up with Jay Rome on a 27-yard pass, North Texas cornerback James Jones was called for interference, and Todd Gurley powered over from the 12 yards out to give Georgia a 7-0 lead.
The Bulldogs made it 14-0 on the first play of the second quarter from their own 2-yard line. Davis beat his man, hauled in the pass, and pulled away from the defense to beat the previous school record of 93 yards, which had been done three times - including the famous touchdown pass from Buck Belue to Lindsay Scott against Florida during the 1980 national championship season.
The teams traded quick scores - Smith's TD was matched by Murray's 16-yarder to Lynch - before Chancellor stunned the crowd on the ensuing kickoff.
One of the nation's top returners, Chancellor found a hole through a wall of blockers, easily slipped past kicker Marshall Morgan, and took off right down the middle of the field for a touchdown that cut Georgia's lead to 21-14.
The Mean Green tied it less than a minute into the second half as the rain began falling heavily at Sanford Stadium. Marcus Trice broke through to block Collin Barber's punt, and Whitfield recovered for a tying TD.