Saints kicker Wil Lutz (3) celebrates his game-winning field goal in overtime. (Jonathan Newton/The Washington Post)

Before injuries, ill-timed drops and defensive lapses caught up with them in the waning minutes of Sunday's game against the heavily favored New Orleans Saints, the Washington Redskins and Coach Jay Gruden showed the grit and guts that have come close to making them winners.

Backed up to their 15-yard line after a brutal third-quarter collision left quarterback Kirk Cousins dazed and broke running back Chris Thompson's right leg, ending his season, Gruden ordered a fake punt. The gamble paid off, and the Redskins rode the momentum from that audacious call to a 15-point lead with less than six minutes remaining.

But the Redskins let New Orleans quarterback Drew Brees lead a comeback that forced overtime, and, in remorseless fashion, the Saints handed the visitors a 34-31 defeat that all but scuttles any remaining playoff hopes.

At 4-6, the Redskins now face a short week to reknit, reboot and prepare to host the New York Giants on Thursday night after a devastating defeat that further battered their already thin ranks.

“It stings,” Gruden said. “It stings a lot of people. It stings everybody involved with the Washington Redskins, that’s for sure.”

In a disconsolate locker room afterward, cornerback Josh Norman, part of a defense that allowed New Orleans (8-2) to roll up 535 net yards and was party to Brees being a flawless 11-for-11 passing on the final two drives, had no words, his head buried under a towel and his back to the room.

And right tackle Morgan Moses, part of an offensive line that has battled through an avalanche of ankle, knee and shoulder injuries, simply couldn’t find words for what it would take to replace Thompson, the pint-size back who has carried the offense in so many ways, leading the team in rushing and receiving.

“You might not be able to replace a guy like that — the things he brings to the offense, to special teams,” Moses said of Thompson, who was surrounded by teammates on the field as his right leg was immobilized in an air cast, then loaded onto the cart. “Just the guy he is in the locker room — it’s hard to lose a guy like that.”

For much of the afternoon, the Redskins had silenced the crowd of 73,138, jumping to an early lead after safety D.J. Swearinger intercepted Brees (29 of 41 for 385 yards, two touchdowns, one interception) on his third throw. It was just Brees’s fifth interception all season. And though the lead teetered back and forth, the Redskins appeared in command with 5:58 remaining, poised to snap the Saints’ seven-game winning streak. All they had to do was preserve a 31-16 lead.

That’s when Brees, 38, proved his Hall of Fame mettle. He didn’t miss a throw on an eight-play touchdown drive that put the Saints within 31-23 with 2:53 remaining.

And for the first time all game, the Redskins’ offense went three and out after losing one yard on a third and one. Washington punted, putting the game in the hands of its defense.

It looked as if cornerback Kendall Fuller sealed it with an interception, but he was called for illegal hands to the face instead. Brees, unflinching, fired an 18-yard touchdown throw to rookie Alvin Kamara, who then ran for the two-point conversion that knotted it at 31 with 1:05 remaining.

In a furious effort to win it in regulation, Cousins drove the Redskins to the New Orleans 34, on the edge of field goal range, but an intentional grounding penalty backed them up. Cousins then dropped back to pass when safety Vonn Bell flew in for a sack that jarred the ball loose. Moses dove on it as time expired.

Overtime only exaggerated the fundamental differences between the teams.

The Redskins, who got the ball first, couldn’t muster a first down. It was two drops and a sack, then a punt.

The Saints, in turn, marched at will against a Redskins defense that had given up 484 yards in regulation. Running back Mark Ingram ran behind left tackle for 20 and 31 yards, setting up the 28-yard field goal by Wil Lutz that clinched it.

Cousins battled throughout, finishing 22 of 33 for 322 yards and three touchdowns, and he acknowledged afterward that he was puzzled by the intentional grounding call on the ball he fired at wide receiver Jamison Crowder.

Rookie running back Samaje Perine impressed, gaining 117 yards on 23 carries, with one touchdown, in his first start after Rob Kelley was lost for the season with knee and ankle injuries.

But the gut-wrenching exacted a high price. Along with Thompson, the Redskins lost safety Montae Nicholson to a concussion. Guard Shawn Lauvao exited after aggravating a shoulder injury, and defensive lineman Terrell McClain left the game with a toe injury.

Brees was best when it mattered most, and he was helped throughout by a 160-yard Saints rushing effort and by facing a defense that just wasn’t stout enough, giving up 535 yards of offense and a staggering 8.1 yards per play.