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 two 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 with Atlanta. ‘‘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 this one out, but Jabari Greer made a diving, touchdown-saving 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 had given up two long passes earlier in the game that led to Atlanta scores.
The Falcons’ 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 with Tony 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.
Both Graham and his Atlanta counterpart, the veteran Gonzalez, were superb in a game that showcased all the intensity and momentum changes expected from such a passionate and longstanding rivalry.
Gonzalez finished with 11 catches for 122 yards and two scores, becoming the first tight end to catch 100 touchdown passes.
Drew 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’s 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 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, Atlanta had just 46 on the ground.
New Orleans rushed for 148 yards, highlighted by Chris Ivory’s 56-yard scoring run that gave the Saints a spark after Atlanta had built a 10-0 lead.