The Bulldogs (2-1) outscored North Texas (2-2) 24-7 in the second half of their first game this season against an unranked opponent.
Murray ran for a touchdown and hit Reggie Davis for a 98-yard TD play, the longest in school history.
Derek Thompson threw for 202 yards and a score for North Texas. Brelan Chancellor ran a kickoff back 99 yards to cut Georgia's lead to 21-14 in the second quarter, but the Mean Green was held to 7 yards rushing in the game.
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