NEW ORLEANS — Needing to redeem himself in the closing minutes of Sunday’s game with the Atlanta Falcons, New Orleans Saints cornerback Jabari Greer came up with the one play he said may have saved his job.

Greer joked that he thought that he was going to be released before breaking up a pass intended for wide receiver Roddy White, capping a goal-line stand with 1:42 remaining that helped secure a 31-27 victory over the previously-undefeated Falcons in a noisy Mercedes-Benz Superdome.

With the Falcons facing a fourth-and-goal from the Saints’ 2, Greer drew a bead on White — the Falcons’ best receiver — and jumped in front of him to bat down Matt Ryan’s pass and preserve their four-point lead.

“I was kind of depressed before that play,” said Greer, a nine-year veteran who is regarded as the Saints’ top cover corner. “I saw my name on the waiver wire. Being able to go out and make a play for our team, and to celebrate after everything that happened. … Just to win that way is a gift.”

It was easy to tell, however, that Greer didn’t want the story of the Saints’ fourth win in five games to be about him.

He gave up two long passes of 49 yards to White, which led to a Falcons’ touchdown on their first possession, and a 52-yarder to Julio Jones that set up a field goal on their previous fourth-quarter drive — allowing the Falcons to slice a 28-17 deficit to one point at 28-27.

“We made something happen,” said Greer, “but the real story is the resiliency of this team and the never-say-die attitude.”

After the Saints (4-5) extended their lead to four points on a 31-yard field goal by Garrett Hartley with 5:54 remaining, the Falcons, who led 10-0 less than six minutes into the game, looked like they were going to come back.

The Falcons (8-1) marched from their own 20 to the Saints’ 10, where Ryan, who was 34-of-52 for 411 yards in leading his team to 454 total yards, hit Harry Douglas for a 9-yard gain to the 1 at the two-minute warning.

At that point, free safety Malcolm Jenkins knocked down a pass intended for tight end Tony Gonzalez, who had 11 catches for 122 yards and touchdowns of 2 and 6 yards, and defensive end Will Smith dropped running back Michael Turner for a 1-yard loss to bring up fourth down.

That’s when Ryan scanned the end zone and tried to go to White, who had seven catches for 114 yards.

But this time it didn’t work.

“It was a play we saw on film,” said Greer. “I was fortunate to be able to make the play. It was something we saw on film study throughout the week.”

It was a fitting way to end the day for the NFL’s 32nd-ranked defense even though it gave up more than 400 yards for the ninth consecutive game.

“The defense stepped up in some crucial situations today,” said Jenkins, who led the Saints with 10 tackles and also broke up three passes. “We made the plays we needed to make when we needed them.”

The Saints certainly needed them at the end as the Falcons used their timeouts and got the ball back with 37 seconds to play. But after one completion, Ryan missed on three straight passes to end it.

The ending was certainly better than the beginning for the Saints, who trailed 10-0 with 9:19 to play in the opening quarter.

Drew Brees threw an interception to Falcons cornerback Asante Samuel on their first play, which resulted in a 37-yard Matt Bryant field goal after Ryan drove his team 80 yards to a 1-yard TD pass to tackle Mike Johnson, who had lined up an as extra tight end.

But the Saints bounced back and had touchdown drives of 78, 90, 69 and 81 yards, which were sandwiched around Ryan’s 2-yard TD to Gonzalez — which was the 100th of his 16-year career.

Chris Ivory, who had 72 yards on just seven carries, had a highlight-reel 56-yard scoring run to get the Saints on the scoreboard.

He out-ran Samuel to the edge and avoided a would-be tackle by safety Thomas DeCoud near the sideline before cutting back to the middle of the field. There, he stiff-armed cornerback Dunta Robinson at the 15 en route to the end zone.

“He’s a beast,” Brees said of Ivory, who was inactive for five games and didn’t played in two others before getting a chance when Darren Sproles went down with a fractured hand. “On more than one occasion, he stiff-armed somebody, or ran somebody over, or cut back on somebody.

“He’s a rare combination of speed and power.”

Brees then connected on a 29-yard TD pass to tight end Jimmy Graham to cap a 90-yard drive before Ryan tossed the first of his two scoring passes to Gonzalez to regain the lead at 17-14.

But Brees and the Saints took the lead at halftime when he found Graham, who had seven catches for a career-high 146 yards, for a 14-yard TD with 34 seconds left.

Then, Brees, who got some help from a running game that picked up 148 yards and 5.1 yards per carry, teamed up with Marques Colston for a 7-yard TD to push the lead to 28-17 before the Falcons tried to come back.

But that’s where the defense, which also held the Falcons to 46 rushing yards and a 2.6 average on 18 carries, stepped in and saved the day — helping the Saints to their 13th straight win in November going back to 2009.

“It’s tough and very frustrating,” said White. “We get all the way down there to the 1-yard line and we expect to score. We just didn’t get it done, that’s the most disappointing thing.

“It’s not like they came out here and won a game today. I think we kind of gave it to them. It’s nothing they did … it was what we did.”

But while White’s words rang hollow in the Falcons’ locker room, Saints interim coach Joe Vitt knew who to credit.

“It was huge,” he said of the goal-line stand. “We made plays when we had to make plays defensively. The two last drives, they had a chance to go in and win .. and everybody kept their poise.”