Atlanta put together a strong drive at end the game but Matt Bryant's 52-yard field-goal attempt sailed wide left. Bryant made two field goals in the second quarter, one from 39 yards and one from 24. The Falcons got the ball with five seconds left but their final play came up way short.
"Two teams with history, regardless of the records it's always been a close game," Saints Coach Sean Payton said. "It's a good win for us. We'll enjoy it for now ... and then get ready for our next game."
The Saints moved to 9-2 with the win and the loss dropped Atlanta to 2-9.
Brees finished the game 23 of 33 for 276 yards and the two TDs. In the first quarter, Brees surpassed Warren Moon to now rank fifth in NFL history in passing yardage. Brees finished the night with 49,566 career passing yards. He ranks behind Brett Favre (71,838), Peyton Manning (63,059), Dan Marino (61,361) and John Elway (51,475).
Graham had another big game with five receptions for 100 yards, his sixth 100-yard game of the season.
The Saints were excellent on third down, converting 7 of 13 chances, and didn't have a turnover. The Falcons' one turnover, a fumble by Darius Johnson forced by
Atlanta quarterback Matt Ryan was 30 of 39 for 292 yards with no TDs and no interceptions but the Saints were able to sack him five times, 2.5 times by defensive end
Roddy White had just two catches for 24 yards and veteran tight end Tony Gonzalez had four catches for 43 yards.
The Saints will have some extra time off before taking on the NFC-leading Seattle Seahawks (10-1) in a "Monday Night Football" game on Dec. 2 in Seattle.