Murray's 24-yard scoring toss with early in the fourth quarter was his fourth of five scoring tosses and put the Bulldogs (12-2) ahead to stay as Georgia scored the game's final 21 points.
Murray finished 18-of-33 through the air for 427 yards and a pair of interceptions as Georgia completed its first 12-win season since 2002.
Chris Conley made scoring grabs of 87 and 49 yards and Tavarras King added three catches for 104 yards and a TD in the victory.
Todd Gurley carried the ball 23 times for 125 yards with a score while Marshall picked up 36 yards on eight rushes for the Bulldogs.
Taylor Martinez completed 16-of-27 passes for 204 yards and a pair of TDs for the Cornhuskers (10-4), but was also picked off twice as Nebraska dropped its third straight bowl game.
Rex Burkhead amassed 140 yards with a score on 24 carries in the loss.