The Falcons started with the ball on offense and moved it well until they approached the endzone, when the Bears' defense tightened, which forced the home side into a 52-yard field goal from Matt Bryant.
Chicago had similar difficulties in finding the endzone as they moved seamlessly downfield, but Jay Cutler couldn't find a target for a seven-point score, and Robbie Gould was brought on to make the 25-yard kick.
The Bears did find the endzone later in the quarter as Brandon Marshall put them in position when he hauled in a 47-yard pass from Cutler. The quarterback then found Josh Morgan for a three-yard score on a slant route.
The visitors could have moved further ahead just before the break but they were unable to find the endzone from inside the 20, although Gould did add another three points with a 28-yarder.
In the second quarter, the Falcons got themselves back into the match when Ryan fired a short completion to running back Antone Smith, who beat his man and two others to find the endzone from 41 yards.
Mike Smith's side levelled the scores when Bryant nailed a kick from 54 yards to put them right back in the match.
However, the Bears rallied right back at the home side and retook the lead when Cutler moved his team into the red zone, and from six yards out handed the ball to Matt Forte, who powered over for the touchdown.
Chicago pulled away from the Falcons when Forte notched his second score of the game when he ran into the endzone from nine yards, while Cutler and Martellus Bennett combined to add the two-point conversion, which was enough to claim the victory.