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NEW ORLEANS -- The Atlanta Falcons can forget about perfection, thanks to their resurgent rivals from the City that Care Forgot.

Of all the teams to end Atlanta's unbeaten run, it had to be the New Orleans Saints. And it had to be a memorable, drama-filled game that left the Falcons frustrated by the 1 meager yard they could not get to take a lead inside the final 2 minutes of a 31-27 loss Sunday.

"It's very frustrating," said Falcons coach Mike Smith, who is 2-7 against the Saints and 49-15 against the rest of the NFL in his four-plus regular seasons as Atlanta coach. "We were close. ... This will be something we will learn from."

If the Falcons (8-1) want to beat the Saints (4-5) in their rematch in Atlanta on Nov. 29, it would help to learn how to stop dynamic young tight end Jimmy Graham, who caught seven passes for a career-best 146 yards and two touchdowns.

Still, Atlanta might have pulled it out, but Jabari Greer made a diving, touchdown-saving pass breakup on a late fourth-down pass intended for Roddy White.

"It's not like they came out here and won a game today," White said. "I think we kind of gave it to them. ... We play them in three weeks and we'll be ready."

Greer's play represented a measure of redemption for the veteran, who'd given up two long passes earlier in the game that led to Atlanta scores.

"I was kind of depressed before that play," Greer said. "I saw my name on the waiver wire. ... Being able to go out there and make a play for our team and be able to celebrate after everything that happened and just to win that way, it's a gift."

Matt Ryan was 34 of 52 for a career-best 411 yards and three touchdowns with one interception. The game was there for him to win when his 9-yard pass to Harry Douglas gave Atlanta a second-and-goal at the 1. But Ryan could not connect on a second-down pass for Gonzalez, the Saints stuffed Michael Turner for a 1-yard loss on third down, and then came Greer's play.

"I could put that ball in a better spot -- a little higher and more in front of him to give him a chance to catch it," Ryan said. "We've always played them tough and haven't had the outcomes we wanted."

Both Graham and his Atlanta counterpart, veteran tight end Tony Gonzalez, were superb in a game that showcased all the intensity and momentum changes expected from such a passionate and longstanding rivalry.

"Tony, he kind of paved the way for me," said Graham, who like Gonzalez had a college basketball background. "It seemed like every drive I'm kind of going up against the things that he did the last drive."

Gonzalez finished with 11 catches for 122 yards and two scores for Atlanta, becoming the first tight end to catch 100 touchdown passes.

Brees threw for 298 yards and three TDs as the Saints won for the fourth time in five games, keeping alive hope of getting back into the wild-card race after an 0-4 start. It was also New Orleans' 11th win in 13 games against Atlanta since Brees joined the Saints in 2006.

The Saints can even their record with a win at Oakland next weekend.

"That's something we feel like we're capable of and we envisioned being able to do that, because we know the type of team we have," Brees said. "We knew we dug ourselves a hole. We knew we had a mountain to climb, but we also knew we have the right type of people."

The Saints still had to punt the ball back to Atlanta with about 40 seconds left, but Gonzalez could not handle a fourth-down throw in tight coverage along the sideline.

"No one is going to go around crying or panicking or anything like that," Gonzalez said. "We're a good team. Our confidence hasn't changed."

Although the Saints came in allowing a league-worst 176.5 yards rushing per game, they held Atlanta to 46 yards on the ground.

New Orleans rushed for 148 yards, highlighted by Chris Ivory's career-long 56-yard scoring run that gave the Saints a spark after Atlanta had a 10-0 lead.

Ivory used a hesitation move to get to the corner past Asante Samuel, broke a tackle by Thomas DeCoud, kept his balance, cut back and then stiff-armed Dunta Robinson before trotting into the end zone.

The Saints' largest lead was 28-17 on Brees' scoring strike to Marques Colston, the 55th of Colston's career, tying Deuce McAllister for first in Saints history. The touchdown capped an 81-yard drive which started with rookie Corey White's interception.

The Falcons pulled to 28-27 on Gonzalez's second TD and Matt Bryant's field goal after New Orleans' second red zone stand of the game.

New Orleans briefly interrupted Atlanta's momentum when Graham's 46-yard catch set up Garrett Hartley's 31-yard field goal.

Atlanta opened the game with an 80-yard scoring drive, highlighted by White's 49-yard reception to the New Orleans 1, setting up an easy TD toss to eligible offensive tackle Mike Johnson.

Samuel then made a diving interception of Brees' first pass and returned it to the Saints 12. However, Samuel drew a penalty for taunting fans, moving the Falcons back to the 27 and Bryant kicked a field goal.

New Orleans vaulted into the lead with touchdowns on two straight possessions, the first on Ivory's long run and the second on Brees' first TD connection with Graham from 29 yards.

The Falcons pulled back in front on Gonzalez's 1-yard catch, capping a drive on which Atlanta converted three times on third down -- all on Gonzalez catches.

Then Graham helped New Orleans regain the lead before halftime, making three catches for 47 yards, the last a 14-yard TD to make it 21-17 at halftime.

Game notes

Ivory's 56-yard run was the longest from scrimmage by a Saint since Oct. 8, 2006, when McAllister ran 57 yards vs. Tampa Bay. ... Ivory's previous career-long run was a 55-yard score at Cincinnati in 2010. ... Brees has now passed for touchdowns in 52 straight games, extending an NFL record he set earlier this season. ... Julio Jones missed much of the first half after an undisclosed leg injury, but returned in the second half. ... Gonzalez now has 101 career TDs, one of only eight players ever with 100 or more. ... All 55 of Colston's TD passes were thrown by Brees, tying the tandem for ninth with Joe Montana and Jerry Rice with San Francisco and Dan Marino and Mark Duper with Miami.