Defensive end Charles Johnson sealed the win by stripping State quarterback Michael Henig of the ball at the Georgia 23 and recovering the fumble.
The freshman Stafford set career-high totals for attempts (32), completions (20), yards (267) and touchdown passes (two) in Saturday's game.
With the win, Georgia improved to 6-2 overall and 3-2 in the Southeastern Conference. State dropped to 2-6 and 0-4. Georgia will meet Florida next Saturday in Jacksonville.
Stafford fired second-quarter scoring passes of 21 yards to tight end Tripp Chandler and 11 yards to receiver Mohamed Massaquoi. The 21-yarder to Chandler came on a fourth-and-1 situation and was the first catch of the sophomore tight end's career. Massaquoi's scoring catch was set up by his own 24-yard reception the play before.
Fullback Brannan Southerland and tailback Kregg Lumpkin each had rushing touchdowns for Georgia. Southerland ran in from a yard out on the first play of the fourth quarter. Lumpkin's 2-yard touchdown in the first quarter opened the day's scoring. The drive was set up by safety Tra Battle's 53-yard interception return and was aided by Stafford's 41-yard pass to receiver Kenneth Harris, career bests for each player.
Kicker Andy Bailey went 3-for-4 on extra points for Georgia.
For State, halfback Anthony Dixson posted three rushing touchdowns. His runs covered five, five and three yards. Kicker Adam Carlson, who tacked on the extra point, later added a 36-yard field goal.