New Orleans Saints tight end Jimmy Graham (80) celebrates his touchdown reception with quarterback Drew Brees (9) and tight end David Thomas in the first half of Sunday's game in New Orleans. The Saints handed Atlanta its first loss of the season by a 31-27 margin.

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.

In other games on Sunday:

49ers 24

Rams 24

SAN FRANCISCO — San Francisco and St. Louis played the NFL’s first tie game in four years as kickers from both teams missed overtime field goals.

Seahawks 28

Jets 7

SEATTLE — Russell Wilson threw touchdowns of 38 yards to Golden Tate and 31 yards to Sidney Rice, and Seattle sent the Jets to their worst start since 2007.

Cowboys 38

Eagles 23

PHILADELPHIA — Tony Romo threw a pair of touchdowns, Dwayne Harris had a 78-yard punt return for a score and Brandon Carr returned an interception 47 yards for a TD to lead Dallas over Philadelphia.

Broncos 36

Panthers 14

CHARLOTTE, N.C. — Peyton Manning made sure John Fox’s return to Carolina was a successful one, throwing for 301 yards and a touchdown to lead Denver.

Patriots 37

Bills 31

FOXBOROUGH, Mass. — Tom Brady threw for two touchdowns, Devin McCourty ended Buffalo’s hopes with an interception in the end zone and New England kept Buffalo winless at Gillette Stadium.

Vikings 34

Lions 24

MINNEAPOLIS — Adrian Peterson raced 61 yards for the game-sealing touchdown midway through the fourth quarter, padding his NFL rushing lead with 171 yards on 27 carries for Minnesota.

Buccaneers 34

Chargers 24

TAMPA, Fla. — Josh Freeman threw two touchdown passes and surging Tampa Bay scored on a blocked punt and Leonard Johnson’s 83-yard interception.

Bengals 31

Giants 13

CINCINNATI — Andy Dalton threw a career-high four touchdown passes — each to a different receiver — and Cincinnati ended its four-game losing streak by beating the New York Giants.

Ravens 55

Raiders 20

BALTIMORE — Joe Flacco threw for 341 yards and three touchdowns, and Baltimore set a club record for points.

Titans 37

Dolphins 3

MIAMI — Colin McCarthy returned an interception 49 yards for a touchdown, and four takeaways helped Tennessee rout Miami.

Texans 13

Bears 6

CHICAGO — Arian Foster finished with 102 yards rushing and a touchdown catch, and Houston intercepted Jay Cutler twice before knocking him out of the game with a concussion on their way to a victory over Chicago.