With a Giants' loss to Baltimore, the Cowboys can still punch a playoff-ticket and an NFC East title with a win over the Redskins in the final game of the regular season at Washington.
Tony Romo hit Miles Austin for a 19-yard touchdown pass with 15 seconds left to play, tying the game at 31-31 to force overtime.
Dallas' offense got the first crack in overtime, but a four play drive stalled, giving New Orleans the ball back.
Saints quarterback Drew Brees led a seven play, 72-yard drive that resulted in the winning field goal.
Brees threw for 446 yards and three touchdowns. His counterpart, Tony Romo was 26/43, 416 yards and four touchdowns in a losing effort.
Cowboys wide receiver Dez Bryant was spectacular. The wideout from Oklahoma State caught 9 balls for 224 yards and two touchdowns. Both of Bryant's scores were 58 yard touchdown grabs.
Saints receiver Marques Colston led New Orleans receiving corps with 10 catches for 153 yards.
The win moves New Orleans' record to 7-8. Meanwhile, Dallas drops to 8-7 and is on life support for a wild card playoff birth.