Sean Payton's men took control of the contest by establishing an 18-point lead by half time, and they finished off their opponents in clinical fashion, ending with 626 yards of offense and an NFL record of 40 first downs in a single game.
Dan Bailey kicked the Cowboys in front with a 37-yard field goal in the first quarter, but the home team took the lead for the first time when Drew Brees found Marques Colston.
DeMarco Murray rushed seven yards to restore the visitors' advantage early in the second quarter, but that was to be the last they saw of it.
Pierre Thomas sprinted into the end zone from a Brees pass, before two touchdowns in two minutes from Darren Sproles stamped the Saints' authority on the contest.
Another after the break from Mark Ingram left the Cowboys with a mountain to climb, although Terrance Williams set about doing so with a touchdown to make it 35-17 by the end of the third quarter.
However, Kenny Stills and Thomas went over in the fourth quarter to inflict a demoralising defeat on Jason Garrett's side, who still remain top of the NFC East with a 5-5 record.