Updated Nov. 3, 2009 @ 4:49 p.m. ET

By Brett Martel, AP Sports Writer

NEW ORLEANS (AP) — Drew Brees and the Saints are so good right now they can't even beat themselves.

New Orleans overcame four turnovers for a second straight week to stay perfect with a 35-27 victory over the Atlanta Falcons on Monday night, matching the best start in franchise history.

Brees, responsible for two turnovers, passed for 308 yards and two scores. Pierre Thomas, who fumbled, also scored two touchdowns. Jabari Greer, who got burned for a deep touchdown, also returned an interception for a 48-yard score, helping the Saints improve to 7-0.

Only the 1991 Saints began a season with as many wins.

"We did a lot of things well and yet we did a lot of things that made it close at the end," coach Sean Payton said. "I'm excited to win though. I'm excited to win this game and get to 7-0. It was an important game against a division team and I'm proud of our players. They fought."

Greer's touchdown was the Saints' fifth score on an interception this season, tying a single-season franchise mark set in 1998. Tracy Porter also had an interception on the Saints 1-yard line on a pass tipped by Jonathan Vilma in the fourth quarter, preserving a 28-24 lead after Thomas' fumble had given Atlanta the ball on the Saints 35.

Atlanta's Matt Ryan was intercepted three times, his third consecutive game with at least two picks.

"I'm not concerned at all," coach Mike Smith said of his second-year quarterback. "We're going to be judged on 16 games. Not one game and not three games."

Still, the Falcons stayed in it until the end, getting a 40-yard field goal from Jason Elam with 28 seconds left, then recovering an onside kick. Ryan only had time for a desperation heave in the final seconds, and Darren Sharper turned it into his seventh interception of the season.

Sharper's pick also was the Saints' 16th overall this season, surpassing New Orleans' total of 15 from 2008. The Saints have at least one interception in every game this season.