Gould's game-winning kick came after a Packers turnover late in the fourth quarter and boosted Chicago to a surprising 3-0 start to the season.
The decisive kick was set up when Packers receiver James Jones caught a 12-yard Aaron Rodgers pass but was stripped of the ball by the linebacker tandem of Lance Briggs and Brian Urlacher near the sideline.
Tim Jennings recovered the fumble at the Green Bay 46 and the ball was awarded to the Bears after a Packers challenge.
After Jay Cutler threw a 21-yard pass to tight end Greg Olsen, the Bears ran down the clock to set up Gould's winning kick.
Cutler finished 16-of-27 for 221 yards with a touchdown and an interception, while Rodgers ended 34-of-45 for 316 yards for Green Bay (2-1).
The Packers were whistled for a team-record 17 penalties in the contest.