On the final two drives and in overtime, Drew Brees was 11-11 with two touchdown passes.
Kamara then converted the tying 2-point conversion by taking a pitch around left end. Coach Jay Gruden announced after the game he suffered a fibula fracture and will require surgery. Brees was held to under 200 yards passing for the second time this season and didn't throw a single touchdown.
Thompson entered the game leading Washington in both rushing (277 yards) and receiving (494) and also had scored four touchdowns.
The Saints took over at their 18 and quickly moved into scoring position behind a 36-yard pass to tight end Coby Fleener.More news: Funding for sports programs at question in new tax bill
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Cousins got the touchdown by standing tall against the blitz and throwing a 40-yard strike to Grant, who was 20 yards behind the Saints' secondary on a blown coverage.
Former first-round draft pick Josh Doctson has had his ups and downs over the past year and a half, he now seems to be the developing into the player the Redskins envisioned.
The Saints tied it on a 52-yard field goal by Lutz, but Washington came right back to regain the lead, 10-3, on Cousins' third-down pass to Thompson. The series was kept alive when linebacker Preston Smith hit Brees in the helmet on a third-and-4 incompletion. Klein and safety Keny Vaccaro - and then lost top cornerback Marshon Lattimore after the opening drive to an ankle injury.
Adding injury to insult, Chris Thompson - the team leader in receiving yards and total touchdowns - was carted off the field with an ugly leg injury and did not return.