Leading by four with three minutes to play, the Cowboys had a chance to clinch the game vs the Saints, but wide out Roy Williams fumbled inside the Saints 10 on a pass play from Jon Kitna, and the Saints recovered.
With the air out of the balloon, the Saints marched down the field, hitting a big pass play from Drew Brees to Robert Meachem of 55 yards to the Dallas 12.
One play later with 1:55 left, Brees went to the end zone, hitting Lance Moore with a score to give the Saints a 30-27 lead. Dallas had a chance to tie but David Buehler was wide on a 59-yard field goal in the last seconds, saving the three-point win for New Orleans.
Dallas falls to 3-8, despite outgaining the Saints 457 to 414. They trailed 17-0 before many could finish their Thanksgiving dinners, but rallied with Kitna throwing for 313 yards on 30-of-42 passing.
The Cowboys clawed back into the game with a couple field goals to make it 20-6 at the half, and then Miles Austin got them back in the game with a 60-yard run to close it to 20-13.
New Orleans pushed it to 23-13, but the Cowboys got back to back short TD runs from Marion Barber and Tashard Choice to put Dallas up 27-23 before they killed themselves with the late turnover.
Brees was 23-for-39 for 352 yards with a TD and a pick. Chris Ivory scored twice for the Saints as they built the early lead before the Cowboys rallied.
New Orleans is now 8-3, winners of four in a row.
The Cowboys will be at Indy for a 4:15 EST game next Sunday.