The Saints started in a 7-0 hole when Tim Hightower scored on a 70-yard run on the game's first offensive play.
Brees passed for 247 yards with three touchdowns.
Bush rushed for 84 yards on five carries, scoring one touchdown on a 46-yard first-quarter run, and adding a touchdown on an 83-yard, third-quarter punt return.
Jeremy Shockey caught Brees' 17-yard touchdown pass, a play on which he was injured, while wide receivers Devery Henderson and Marques Colston caught touchdown passes for the Saints (13-3), who ended the regular season with a three-game losing streak.
Hightower led Arizona with 87 yards on six carries.
Beanie Wells scored once, but aging Kurt Warner passed for 205 yards with one interception.
He was injured during his second-quarter interception for the defending NFC champion Cardinals (10-6).