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NEW ORLEANS -- A perfect record would have been lagniappe, as they say in Louisiana -- a little something extra.

The history-making achievement the Saints and their fans really covet is a first Super Bowl appearance, which is all that's left to accomplish now that Tony Romo and Dallas ended their December doldrums at New Orleans' expense.

Drew Brees and the Saints are marching toward an unbeaten season no more after their frenzied rally fell short in a 24-17 loss to the Cowboys on Saturday night.

"This is going to sting for a while but we've got to be able to put this behind us," Brees said, noting that the Saints remain in control to finish the No. 1 playoff seeding in the NFC. "It's all about the next game."

Romo threw for 312 yards, including a 49-yard touchdown to Miles Austin, and DeMarcus Ware punctuated his comeback from a neck injury with a game-sealing strip of Brees.

The loss by the Saints (13-1) left the Indianapolis Colts (14-0) as the NFL's only unbeaten team this season.

"We'll digest this," Saints coach Sean Payton said. "Nonetheless, it is what it is and we've got to get back to work next week. We have two important games in front of us and we'll take that approach."

The Saints' start had New Orleans hoping its team could go 19-0 and win the Super Bowl after so many years of losing and heartbreak. It was seen by some as a symbol of New Orleans' ability to come back better than before from the epic disaster that was Hurricane Katrina a little more than four years ago.

Brees had sensed all of that, and made no secret that he wanted the Saints to go for it.

"We feel like we deserved it and the whole city deserved it and we wanted to make it happen," Brees said. "That's probably the most disappointing thing about it."

Instead, the Cowboys (9-5) overcame failures of a more recent nature, ending a two-game skid and proving they were good enough to beat the top team in the NFC in front of a charged-up, hostile crowd. They came to New Orleans 3-8 in December games in their last three seasons under coach Wade Phillips, who was finding himself increasingly on the defensive about his club's ability to play well down the stretch.

Dallas dominated early, scoring on its first two possessions to take a 14-0 lead and went up 24-3 on Marion Barber's second short TD run of the game in the third quarter. Then the Cowboys held on despite Nick Folk's surprising missed 24-yard field goal shortly before the 2-minute warning.

"I said all along this team has a lot of heart, a lot of character and a lot of leaders," Phillips said. "I didn't think this team could get beat three times in a row."

The high-powered Saints nearly pulled off what would have been the latest of several improbable comebacks.

Mike Bell's 1-yard run made it 24-10 with 12:35 to go. Brees followed that by capping a seven-play, 70-yard drive with a 7-yard touchdown pass to Lance Moore with 8 minutes left, cutting New Orleans' deficit to 24-17.

That left it up to the Saints' defense to hold once more. Dallas faced a third-and-7 on its own 23 and the crowd was going so wild Romo had to call timeout a moment before the play clock expired.

The noise was still deafening when Romo returned to the line of scrimmage, but that didn't stop him from finding Austin on a short crossing route for a 32-yard gain.

"We did what we knew we had to do on that drive," Romo said. "We all know how good their offense is so we had to move the ball on them."

On the next play, Romo spun away from the rush and hit tight end John Phillips for a 23-yard gain to New Orleans' 22. From there, Dallas went conservative and set up what looked to be a game-sealing field goal from nearly the same distance as Shaun Suisham's miss two weeks ago, which allowed the Saints to come back and beat Washington in overtime.

When Folk's kick bounced off the upright, the crowd erupted, sensing the Saints were simply destined not to lose. And it looked that way after Brees converted a frantic fourth down on a pass over the middle to Marques Colston, who made a one-handed catch.

The Saints marched to midfield in the final minute, but the Cowboys held firm. Ware stripped Brees for the second time in the game and lineman Jay Ratliff recovered, silencing the packed Superdome while the Cowboys leapt in the air and embraced one another.

"That was a fun one," Romo said. "These are the ones you love to play."

Ware had to be taken to the hospital only a week earlier after what looked like a serious neck injury in Dallas' loss to San Diego. He didn't practice fully all week, but said he was feeling better and was cleared to play. He certainly looked rested and healed.

He sacked Brees twice, forcing fumbles that the Saints' lost both times. The first one set up a field goal that gave Dallas a 17-3 lead at halftime. Linebacker Anthony Spencer also had two sacks.

Very little went right for Brees, who was intercepted once, sacked four times and pressured all night. Even what looked like a certain 36-yard touchdown pass in the third quarter slipped through Devery Henderson's hands in the end zone. Brees was sacked by Spencer soon after and that drive ended with a punt.

Game notes

The Cowboys outgained the Saints, 439 yards to 336, holding the Saints 90 yards and nearly 19 points below their averages in those categories. The Saints, who came in converting nearly 48 percent of third downs this season, converted only one of seven. ... Miles caught seven passes for 139 yards, going over 1,000 yards for the first time in his four-year career. ... Reggie Bush pulled up lame in the second quarter, favoring his right leg, and did not return. The Saints did not provide an update on his condition.