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The Redskins took the lead on their first possession when Cousins fired a short completion to Jordan Reed, who sprinted to the endzone and managed to edge the ball over the goalline to record a 16-yard score.
New Orleans rallied when Drew Brees guided his team downfield before finding Brandin Cooks in the endzone on a five-yard slant, but the parity only lasted until the end of the quarter when Cousins delivered a strike for Jamison Crowder to restore Washington's lead.
Brees was not to be deterred and he along with Cooks brought their side level once again as the quarterback lofted the ball over the middle of the field for the receiver to catch and run for a 60-yard score.
However, the Saints defense suffered a breakdown on their tackling as they allowed Matt Jones to raid 78 yards after receiving a short pass from Cousins to score a touchdown.
Dustin Hopkins took the game away from the visitors as he nailed three field goals in succession after the Washington defense had thwarted Brees's attempts to bring his team back into the contest.
Reed notched his second touchdown of the game late in the third quarter to all-but secure the win for the home side with an eight-yard score.
Dashon Goldson poured further misery on the Saints when he intercepted Brees and returned the ball all the way for a 35-yard touchdown. Hopkins then kicked his fourth field goal of the match to cap the emphatic victory for the NFC East outfit.
The Redskins are now 4-6 in their season, while the Saints fell to 4-6.