Ryan completed 19-of-33 for 185 yards and got intercepted twice.
Michael Turner scored the Falcons' other touchdown on a 5-yard run in the fourth quarter.
The Bears scored TDs on a 23-yard pass from Jay Cutler to Johnny Knox in the second quarter and a 2-yarder from Cutler to Greg Olsen in the fourth quarter.
Chicago mounted a strong comeback attempt in the fourth quarter as Cutler hit Devin Hester three times for a total of 46 yards. A pass-interference call against Falcons linebacker Curtis Lofton with 1:07 left gave the Bears a first down at Atlanta's 14 yard line.
Two penalties pushed the Bears back to the 29 before Cutler's 24-yard pass to Earl Bennett put the ball on the 5 yard line for fourth down and 1. A motion penalty against Orlando Pace cost 5 yards, and Cutler's pass to Desmond Clark fell to the turf, giving the Falcons the win.
2014: NFL Cheerleaders [PHOTOS]
Michael Sam cut from the Dallas Cowboys