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The Redskins went ahead in the contest when Alfred Morris raced through the line for a one-yard touchdown, to record his first rushing score of the season.
The visitors extended their advantage following fine work from Kirk Cousins to move his side into the redzone, and he completed the score by faking the handoff to Morris and running into the endzone himself from five yards.
Chicago got back into the game with 18 seconds left in the half when Jay Cutler avoided the pass-rush and threw deep into the endzone for Alshon Jeffery, who shook off man-coverage to make the catch for a 20-yard touchdown.
The Redskins regained their composure at the start of the third quarter and restored their 14-point lead when Cousins fired the ball into the chest of Jordan Reed for a five-yard touchdown.
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The home side continued to be resilient and marched downfield to pull within seven points as Cutler faked the handoff to Matt Forte before sending the ball into the hands of his tight end Zach Miller for the score.
Forte then brought his side level as he powered through the line to burst through two tackles to find the endzone from seven yards.
The Redskins battled back to regain the advantage as Cousins moved his offense into the range of Dustin Hopkins before the kicker held his nerve to send his 47-yarder through the posts.
Chicago had the chance to level the scores late in the match to send the game to overtime, but Robbie Gould missed his kick, leaving his team to succumb to defeat as the Redskins ran out the clock.
The result leaves the Redskins in first place in the NFC East by improving their record to 6-7, while the Bears drop to 5-8 in their campaign.