Brees racked up four touchdowns in the performance, which gave him 5,087 passing yards for the season -- 3 more than the previous record, set by the Miami Dolphins' Dan Marino in 1984.
Brees will have a chance to add to the record next week as the Saints (12-3) finish their regular season schedule against Carolina -- after clinching the NFC South with Monday's shellacking of the Falcons.
Sproles (233 all-purpose yards) hauled down the record-setting pass.
Atlanta (9-6), the defending division champs, lost for only the second time in six games.
Matt Ryan went 34-of-52 through the air for 373 yards with a touchdown for the Falcons, who dropped both of their games against the Saints this season.