Cutler tied a career high with the four scoring strikes, going 14-of-21 through the air for 247 yards, and Matt Forte picked up 117 rushing yards on 14 attempts for the Bears (8-3).
Earl Bennett grabbed four passes for 56 yards and scored twice for Chicago, which took a one-game lead over Green Bay in the NFC North.
The Eagles (7-4), meanwhile, saw their three-game winning streak halted despite 333 passing yards from Michael Vick, who went 29-of-44 on pass attempts with two scores and ran nine times for another 44 yards.
With the loss, Philadelphia fell into a first-place tie with the New York Giants in the NFC East.
Celebrity Couples of 2014 [PHOTOS]