He and retired quarterback Peyton Manning had been tied with 15 400-yard passing games entering Week 6's games.
Brees also threw four touchdown passes as the Saints dropped the defending NFC champion Panthers to 1-5 this season.
Brees also reached another milestone in Sunday's game, becoming the sixth player to record 50,000 passing yards with one team. The other five are Manning (Colts), Brett Favre (Packers), Dan Marino (Dolphins), Tom Brady (Patriots) and John Elway (Broncos).
ESPN Stats & Information contributed to this report.