The Saints made 40 first downs during the match, the highest total ever in a single NFL game, while they also broke their franchise record for total yards with 625.
Brees himself completed 34 of 41 passes for 392 yards and four touchdowns, and he praised his side's passing and running games as they dominated the Cowboys throughout.
"Spreading the ball around, getting everybody involved - these are the days you love to have. You strive for efficiency both in the run and the pass game. We had that today," Brees told The AP.
The result means that the Saints stay top of the NFC South with a 7-2 record.