FLOWERY BRANCH -- Lost in the stunning 27-25 victory over the Saints on Sunday was the fact that the Falcons blew an 18-point fourth-quarter lead.

The Falcons’ defense struggled in coverage, the offense couldn’t sustain a drive and special teams chipped in with a big penalty and a long punt return that allowed the Saints to take a 25-24 lead with 1:01 to play.

“We didn’t do our job on offense,” Falcons coach Arthur Smith said. “It’s all three phases.”

The Falcons (4-4) are set to play the Dallas Cowboys (6-2) at 1 p.m. Sunday at AT&T Stadium in Arlington, Texas and must show that they’ve learn their collective lessons from the collapse against the Saints.

Falcons quarterback Matt Ryan and wide receiver/running back Cordarrelle Patterson bailed everyone out with a 64-yard pass play that put the team in range for a field goal.

There was one last bullet to dodge, but the Falcons pounced on Mike Davis’ fumble and then kneeled two times to set up Younghoe Koo for a 29-yard game-winning field goal at the buzzer.

“We’ve got to be better in certain stretches,” Smith said. “You don’t want the penalties to happen where you give up short fields in a quick amount of time. Normally, when you are in that situation the clock is to your advantage.”

But with 10:34 to play and the Falcons up 24-6, they imploded.

The Saints zipped 66 yards down the field in 2:42 on eight plays. New Orleans quarterback Trevor Siemian tossed a 5-yard touchdown pass to Marquez Callaway.

Cornerback Avery Williams was in coverage on the big play, a 25-yard pass play to tight end Adam Trautman.

“I was just trying to do my job on that play,” Williams said. “It’s never good when we let them into our red zone. I’m just trying to do my part. There are things to improve.”

The extra point made the score 24-13.

The offense went three-and-out and punted to the Saints. Returner Deonte Harris was body-slammed by Richie Grant, who was called for unnecessary roughness.

Instead of drive starting at the Saints 31, they were in business near mid-field at their 46. On the next play, cornerback Fabian Moreau was called for pass interference on Harris. The 27-yard penalty moved the ball to the Falcons 27.

After two incompletions, linebacker Foye Oluokun sacked Siemian for an apparent 10-yard loss. He was called for roughing the passer as he hit the ducking quarterback’s head after he jumped to block the pass attempt. Instead of fourth-and-20 from the 37, it was first-and-10 from the 13.

“It’s my instinct (to jump),” Oluokun said. “I was trying to do too much.”

Four plays later, Saints running back Alvin Kamara scored on a 2-yard run. The two-point conversion pass was incomplete, and the Falcons led 24-19.

After a holding call on Saints cornerback Bradley Roby (Peachtree Ridge High), Feliepe Franks was dropped for a 1-yard loss on a RPO and Ryan was sacked on second and third downs.

The Saints returned the punt for 26 yards to the Falcons’ 43. Five plays later, Siemian tossed a 8-yard touchdown to Kenny Stills to give the Saints the lead, 25-24. The two-point conversion run by Kamara was stuffed.

The lead evaporated quickly.

Smith was most vocal about the penalty-aided drive.

“When you give them a short field and you punt and add on a 15-yard penalty, then get a DPI, (and) the clock is not moving, they gain a lot of yards,” Smith said.

The collapse was not all on the defense.

“We didn’t do a good-enough job on that drive of handling it,” Smith said. “Then they have a punt returner (Harris) go across the 50. (On) the last two offensive drives, they had really short fields with a lot of penalties.”

Smith is hoping that the Falcons learned their lessons in the victory.

“There’s only so much time left in the game, and in all three phases you have to play clean to finish off a good football team,” Smith said. “Last time I checked, we won the fourth quarter four times.”

There was plenty of blame to go around for the collapse.

“You have to put it on special teams, you have to put it on offense, put it on me,” Smith said of blowing the lead. “But ultimately at the end of the day, we still finished the fourth quarter.”

The Falcons can’t run out the clock because of the poor rushing attack. They are averaging 80.4 yards rushing per game, which ranks 29th of 32 teams in the NFL.

“There are always things to improve on, like we have to get better in the run game,” Smith admitted. “There’s always things. That’s the name of the game if you continue to look objectively.”