I've re-watched the game more than once. They didn't quit. They were just that bad and out of sorts. They had Heath at Safety, Webb/Pellerin as nickel CBs, Bosworth at MLB. Add that to Sims and Carter playing without Lee in to lead them. They even had Everett Brown, the 265 pound DE, playing DT at some points in that game. Ware was limping around and the remainder of the DL are castoffs from other teams and one was a practice squad rookie that had never played in a regular season game.
On offense, once the Saints had a big lead, Rob Ryan could play a high risk style defense that made the Cowboys offense look even worse. He knew the Cowboys were so worried about the pass rush, that his CB completely abandoned coverage on TWilliams to jump a short out route to Witten. A D-Coordinator can cause havoc when his team has a big lead.