After Sproles' TD was wiped off the board, Brees made another huge mistake with New Orleans inside the Atlanta 10, allowing the clock to run out in the first half without at least attempting a field goal.
Four days earlier, Brees had two passes picked off and returned for touchdowns in a loss to San Francisco.
This one was even worse. He finished 28 of 50 for 341 yards but had a rating of just 37.6, the third-lowest off his career.
"I feel we have one of the best secondaries in the NFL," Falcons cornerback Dunta Robinson said, "and I think we came out and showed that."
When the Saints arrived in Atlanta, their bus was pelted by eggs at the airport, epitomizing the long rivalry between the teams. New Orleans had dominated in recent years, winning four in a row and 11 of 13.
This time, Michael Turner scored on Atlanta's opening possession, Tony Gonzalez hauled in a touchdown pass from Matt Ryan, and Matt Bryant booted three field goals, including a 55-yarder.
The defense did the rest.
"We got the monkey off our back," DeCoud said.
After winning so many close games, the Falcons started this one as if they were intent on routing the only team to beat them this season. New Orleans knocked off Atlanta 31-27 at the Superdome on Nov. 11, the bright spot in a tumultuous year that was marred by a bounty scandal and a season-long suspension for coach Sean Payton.
Ryan completed a pass on the first play from scrimmage before turning it over to a running game that has struggled most of the season. Turner burst around right end for a 35-yard gain. Jacquizz Rodgers broke off two straight 14-yard gains. Finally, it was Turner going in standing from 3 yards out, giving Atlanta a quick 7-0 lead.