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The Patriots took the lead on their first drive of the game when Tom Brady fired a short completion to Julian Edelman down the sideline and the wideout made his man miss to dive in for an eight-yard score.
Edelman spurned the chance to add to the scoreline on the next possession following a successful onside kick from the home side, but they were soon presented with the ball back in their possession when Logan Ryan intercepted Redskins quarterback Kirk Cousins.
New England capitalised when Brady handed the ball to LeGarrette Blount and he churned through the line to record a five-yard score.
The Patriots were held out of the endzone by the Redskins' defense on their next possession, but Stephen Gostkowski fired his 21-yard field goal through the posts.
Washington got on the board before the end of the half, but were forced to settle for a field goal from the boot of Kai Forbath.
In the second half, the Patriots once again had no problem coasting downfield, but were held out of the endzone by good play from the Redskins, and were held to three points from Gostkowski's boot.
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New England were dealt a blow when running back Dion Lewis sustained a serious knee injury, but his replacement Brandon Bolden secured the win for his team when he latched on to a deep pass from Brady for an 18-yard touchdown.
Jordan Reed scored a consolation touchdown for the Redskins late in the game as he corralled Cousin's pass, but the match belonged to New England.