Brees completed 26-of-34 for 332 yards for the Saints (6-1), who showed no signs of slowing down coming off a bye week.
One defense, New Orleans pressured Bills quarterback Thad Lewis into three fumbles and picked him off once.
Lewis ended up making good on 22-of-39 passes for 234 yards with a scoring strike as Buffalo (3-5) fell for the third time in four games.
Stevie Johnson made seven grabs for 72 yards with a touchdown while Scott Chandler also compiled 72 yards on seven catches for the Bills.
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