The victory moved Atlanta (3-11) ahead of the Saints (2-12) and the New York Jets, and dropped the Falcons behind those two teams in next spring's draft order.
"We'll worry about the draft when the season is over," Atlanta Coach June Jones said. "It was good to get a win on the road. It makes the flight home a lot better."
Befitting a game between two of the league's worst teams, play was sloppy. The Falcons were penalized nine times for 70 yards and had a touchdown and 84-yard fumble return nullified. The Saints drew 12 penalties for 76 yards.
"For us it was just too much bad ball, really," said Rick Venturi, the Saints' interim coach. "Penalties, fumbles, dropped passes, shoddy tackling--you're not going to be very good in that situation."
Atlanta led, 31-9, in the fourth quarter, and Hebert completed 20 of 29 passes for 198 yards.
New Orleans took a 3-0 lead on Doug Brien's 34-yard field goal midway through the first quarter. The Saints didn't lead again. The Falcons answered with a 68-yard drive that included a 25-yard reception by Craig Heyward, 16- and 14-yard catches by J.J. Birden and a three-yard touchdown reception by Mitch Lyons.
Atlanta stretched the lead to 14-3 with a four-yard touchdown reception by Eric Metcalf 29 seconds before halftime.
Atlanta took the first-half lead despite two interceptions by Hebert and two fumbles.
The Saints were even worse, turning the ball over on an interception and converting on only three of 12 third downs.
"I'm not going to say I'd like to see the season end," Saint tackle William Roaf said. "I'd like the season to end on a positive note. But we're not doing what it takes to win games."