New Orleans answered with a field goal of their own and the teams traded touchdowns before Kirk Cousins completed four passes to set up a Samaje Perine touchdown run that lifted the visitors to another lead early in the second quarter. They then picked up the two-point conversion as Alvin Kamara walked into the end zone untouched.
Thompson was injured while blocking as Cousins ran in his direction.
New Orleans responded on their next possession with a 52-yard Wil Lutz field goal to tie it at 3.
Kamara also passed the 1,000-yard mark in total yards for his rookie season.
Danica Patrick Is Done With Full-Time Racing
Patrick went on to thank members of her team and her family, as well as boyfriend and fellow NASCAR driver Ricky Stenhouse Jr. She has not yet announced which team she will drive for, but did say that she does not anticipate a return to NASCAR.
With 2:53 left in the game Brees hit his first touchdown pass in two games with a 3-yard strike to Jeremy Hill.
In the closing seconds of the fourth quarter, the Redskins moved the ball to a first down at the New Orleans 34 - within range of a potential game-winning field goal - but Cousins was flagged for intentional grounding on first down, moving the Redskins out of field-goal range. They're 4-6 in a conference where it could take 10 wins to make the postseason. But the Redskins quarterback barely missed any time, quickly coming back on the field and tossing a touchdown for what appeared to be the "dagger" TD - Troy Aikman's words - for the Redskins to take a 24-13 lead.
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. Thompson was engaged in a block and had his right leg bend back after he got caught in an awkward position under Saints defensive tackle Sheldon Rankins.
It didn't help matters that the defense was without middle linebacker A.J. Klein and safety Kenny Vaccaro, both inactive, and cornerback Marshon Lattimore, who left the game in the first quarter with an ankle injury.