Brees, who missed New Orleans' previous game because of a bruised rotator cuff in his right (throwing) shoulder, completed 32 of 39 throws for 279 yards in his return.
Mark Ingram gained 126 yards from scrimmage on a combination of runs and short passes, and Khiry Robinson had a 1-yard touchdown run for New Orleans (1-3).
Joseph Randle scored the lone TD for Dallas (2-2) on a 1-yard run in the first half. The winning score enlivened a Superdome crowd stunned by Saints kicker Zach Hocker's 30-yard miss in the final seconds of regulation.