Brees, who completed 26-of-35 passes, connected with Jimmy Graham on a 7-yard touchdown pass with 6:22 left in the third quarter to put the Saints ahead for good.
The defense took over from there, stopping the Falcons without a point in their last four drives as New Orleans (1-0) won in the return of Coach Sean Payton to the sidelines after a yearlong suspension in connection with the Saints' "bounty" scandal.
Atlanta (0-1) was led by Matt Ryan, who went 25-of-38 through the air for 304 yards, two touchdowns and a key late-game interception.
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