NEW ORLEANS -- If this winds up being a special season for the New Orleans Saints, they will point back to Sunday’s win over the Washington Redskins for years.

Just like 2009 all over again.

The Saints (8-2) had no business winning their eighth straight game Sunday after trailing by 15 points with less than three minutes remaining -- just like those ’09 Super Bowl Saints had no business coming back from a 10-point deficit at Washington in the fourth quarter. Fittingly, the hero of that game -- receiver Robert Meachem -- served as the honorary captain on Sunday.

"I would say, when you have wins like this, it's the No. 1 thing you'll miss when you're finished playing or you're finished coaching -- the excitement of getting one that maybe you didn't think you were going to get," said Saints coach Sean Payton, who said the comparison to that 2009 game was "fair" -- and even mentioned the same to his team in the postgame locker room -- though he said, "We'll see" if this year's version has the same DNA.

In the same breath, though, Payton didn't let the Saints off the hook for the miscues that led them to trailing 31-16 in the first place.

"There's a lot of things we've got to get cleaned up. There's no 'Victory Monday' tomorrow. We'll be in early tomorrow ... and that's just how it's gonna be," Payton said.

It was far from the Saints' prettiest or cleanest victory. But sure enough, two quick touchdowns, three defensive stops and a field goal in overtime led them to a 34-31 victory and kept them flying as the hottest team in the NFL (even on their worst day).

Saints running back Mark Ingram rushed for 134 yards and a touchdown in Sunday's overtime win over the Redskins. Sean Gardner/Getty Images

It was the first time in Saints history that they had ever come back from a 14-point deficit in the fourth quarter, according to the Elias Sports Bureau.

The Saints’ dynamic run game played a huge part -- with Mark Ingram running the ball twice in overtime for 20 and 31 yards to set up the game-winning field goal and Alvin Kamara running in the game-tying 2-point conversion in the final minutes of regulation behind a great block by tight end Josh Hill.

But Drew Brees also had his finest moment of the year, completing 11 of 11 passes for 164 yards and two touchdowns on the Saints’ two quick touchdown drives at the end of regulation. The Saints haven’t asked Brees to be Superman during their win streak because the defense and run game have been so good, but he sure played the role when needed on Sunday. Tight end Coby Fleener also came up huge, among others, on those drives. And Kamara’s bobbling 18-yard TD catch went from a possible disaster to a thrilling moment.

"Just finding different ways to win," Brees said. "We haven’t encountered a game like this in a while, and it was great to watch the team rally, come together. These are wins that you build on and develop confidence ... and you realize we can win anywhere, anytime.

"A game like this, we’re gonna grow and become stronger from and gain more confidence from versus last week [a 47-10 rout at Buffalo]."

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The Saints' defense, meanwhile, came up huge on the final three stops after a rough day with four key starters missing (safety Kenny Vaccaro and linebacker A.J. Klein were inactive; cornerback Marshon Lattimore left in the first quarter with an ankle injury; defensive end Alex Okafor left late in the fourth quarter with an unspecified leg injury).

They gave up two wide-open TD passes in the second half and a 26-yard pass on a gutsy fourth-and-6 call by the Redskins in the second quarter, among other miscues.

But in the end, they came up with a huge third-and-1 run stuff when the Redskins almost ran out the clock near the end of regulation; then they forced an intentional grounding penalty and a sack in the final minute of regulation to knock the Redskins out of field goal range; then they forced a three-and-out when Washington got the ball first in overtime.

Special teams got in the mix, too. Tommylee Lewis had a 24-yard punt return on a fourth-quarter field goal drive and a 14-yard punt return in overtime -- in his first two punt returns of the season. And kicker Wil Lutz made all four of his field goal attempts, including the game-winning 28-yarder in overtime.

"Enough guys did enough good things. I'm proud of how they hung in there," said Payton, whose message about the 2009 team hit home with the 50 players on this current 53-man roster who weren't around to experience it.

"That’s one of the things that defines a winning team," Saints defensive end Cameron Jordan said. "Every win wasn’t pretty, but they got those close wins."

The Saints will now face one of their most challenging matchups (on paper, at least) throughout this two-month run -- a trip to Los Angeles to face the 7-3 Rams next Sunday.