Falcons quarterback Matt Ryan connected on 24-of-28 pass attempts, good for 198 yards and a score, and running back Michael Turner rambled for 110 yards and a touchdown on 23 carries for the Falcons (9-2).
Tony Gonzalez grabbed six balls for 51 yards and a touchdown, helping the Falcons post their fifth straight victory and stay one game ahead of New Orleans atop the NFC South.
The Packers (7-4), meanwhile, saw their four-game winning streak snapped.
Aaron Rodgers amassed 344 yards and a TD, going 26-of-35 through the air and rushing the ball 12 times for 51 yards and a touchdown. He found Jordy Nelson for a TD pass in the final minute to forge a short-lived tie.