McCown, making his fourth consecutive start in place of Jay Cutler, threw four touchdown passes and ran for another in frigid conditions at Soldier Field in Chicago.
McCown was 27-for-36 for 348 yards, while Forte carried the ball 20 times for 102 yards and added seven catches for 73 yards and a score.
The Bears improved to 7-6 and snapped a two-game losing streak.
The Bears moved into a tie with Detroit for first place in the NFC North. But Detroit hold the tiebreaker as they beat Chicago in a pair of games this season.
Tony Romo threw 11-for-20 for 104 yards and had three touchdown passes for the Cowboys.
Dallas, who had won their previous two contests, dropped to 7-6 for the season.
The Cowboys fell into second place in the NFC East and one game behind the Eagles, who defeated the Lions on Sunday.
Cutler is out with a sprained ankle and the Bears also played without star linebacker Lance Briggs.
Chicago's win levels the all-time series between the clubs at 11-11. The Bears have won the past three, including a 34-18 victory in October last year.
The teams haven't met in Chicago since September 2007 when the Cowboys won 34-10.
Chicago retired hall of famer Mike Ditka's number at halftime in a chilly ceremony during which temperatures dipped to around -18 degrees (Celsius) with the wind chill.