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The Redskins advanced inside the 20-yard of the Eagles in the early stages of the game thanks to a series of runs from Chris Thompson, but the home side failed to punch the ball in the endzone, resulting in a field goal from Dustin Hopkins to hand them a three-point lead.
Washington extended their lead through the boot of Hopkins as he sent his kick between the posts from 38 yards after Cousins has engineered a drive to put them on the edge of the redzone.
The Redskins continued to dominate as Cousins and Thompson found further success on offense, and although the quarterback fumbled the snap on the goalline, he managed to recover it to score the touchdown.
Philadelphia had the chance to get on the board just before the break, but Caleb Sturgis sent his 33-yard field goal wide of the posts to leave his side scoreless at the halfway stage.
In the second half, the Eagles got off the mark in the match when Sam Bradford threw deep to the endzone for Riley Cooper to make the grab for the 62-yard score, but Sturgis failed to score from the extra point.
Bradford began to find his rhythm and brought his side back into the game as he found tight end Brent Celek in the endzone for a 10-yard score, and this time Sturgis nailed the extra point to bring the visitors level.
The Redskins responded when Hopkins converted his third field goal of the match to put the hosts ahead. However, Bradford struck at the beginning of the fourth quarter when he found Miles Austin in the endzone to fire his side ahead for the first time in the game.
Cousins waited until the final possession of the game to produce his best form as he moved his side to the goalline before finding Garcon for a three-yard score to win the match for his side.