Trailing 31-17 with under five minutes left, Romo directed an 80-yard drive, capped by a 16-yard TD pass to Dwayne Harris.
After forcing a Saints punt, Dallas took over at its own 36 with 1:29 remaining. On fourth down, Romo threw a 19-yard to Miles Austin to tie the game 31-31 with 15 seconds left.
“This one was tough,” said Jason Witten, who broke the NFL single-season receptions record for a tight end. “Games come down to a handful of plays, especially for us this year ... We've got to move forward. We (still) have an opportunity to go to the playoffs.”
Dallas' defense is banged up heading into its winner-take-all showdown. Defensive star DeMarcus Ware missed most of the fourth quarter with a nagging sprained shoulder but is expected to play against the Redskins.
The Cowboys have been relying on Romo and a high-powered offense that currently features one of the league's hottest quarterback/receiver combos.
In Sunday's loss, former OSU standout Dez Bryant hauled in nine passes for a career-high 224 receiving yards, highlighted by two 58-yard touchdowns in the first half.
Having scored at least one touchdown in seven consecutive games, Bryant has accumulated 46 catches for 808 yards and 10 TDs the past seven games.
One negative was running back DeMarco Murray fumbled for the second consecutive week. This one was costly.
Former OU teammate Curtis Lofton stripped Murray late in the third quarter. Lofton recovered the fumble at the 5-yard line to set up the Saints' go-ahead score. On its next possession, New Orleans went 80 yards for a 31-17 lead.
But similar to recent wins over Cleveland, Cincinnati and Pittsburgh, the Cowboys rallied.
“That's kind of how it's been all year,” Austin said. “We're going to keep fighting until the end. Unfortunately we fell a little short today.”
The reason the Cowboys still control their own destiny is if they defeat Washington both teams would finish 4-2 in the division. The next tiebreaker is record versus common opponents. With a win, the Cowboys would be 8-4, the Redskins 7-5.
Despite the loss, the Cowboys caught a break.
“Nothing is a big break when you have to play on their home field,” Murray said. “That's going to be a hard team to beat. It won't be easy. We just have to have a short-term memory and move on.”