Trailing 14-0 in the second quarter, the Packers scored the game's final 25 points to win going away.
Rogers connected on a 70-yard scoring strike to James Jones late in the third quarter, giving the Packers their first lead at 15-14, and hooked up with Greg Jennings on a 29-yard score less than 5 minutes later to seal the win.
Mason Crosby booted four goals for Green Bay (5-0), which won its 11th straight game dating back to last season.
Jones finished with five catches for 140 yards.
Matt Ryan was held to 18-of-32 through the air for 167 yards for the Falcons (2-3), who also lost to the Packers in a divisional playoff game last season.