If nothing else, the Dallas Cowboys have been an accommodating opponent for the New Orleans Saints ever since coach Sean Payton took charge in New Orleans in 2006.

The Saints have won four of their five meetings against Dallas in the past eight years — and all three in the past four seasons. Quarterback Drew Brees has thrown 14 touchdowns and two interceptions against them for the Saints.

Yet the Cowboys (2-1) and Saints (1-2) who will meet at 7:30 p.m. Sunday in AT&T Stadium look a bit different than they did when Dallas was routed 49-17 in New Orleans last Nov. 10. Complicating matters for the Saints is that they have lost seven of their past eight regular-season games on the road, including two this year (37-34 in overtime in Atlanta and 26-24 in Cleveland).

All of which left the Saints in no mood this week to beat their chests about the way they’ve been getting the upper hand on the organization that proclaims itself “America’s Team.”

“This team right here ... hasn’t done anything to Dallas,” said receiver Robert Meachem, who’s in his seventh season with the Saints. “So we can’t even think about the past.”

In the past resides the time Payton’s 2006 Saints visited the Cowboys of coach Bill Parcells, under whom Payton had worked in Dallas from 2003-05. The Saints thrashed Dallas 42-17 en route to their first appearance in the NFC Championship Game.

But don’t forget the times the Saints salvaged victories out of what seemed to be sure defeats on Thanksgiving Day 2010 and the afternoon before Christmas Eve in 2012.

On the first of those occasions, the Saints saw a 20-3 lead with 43 seconds left in the first half turn into a 27-23 deficit with 5:51 to go. In their third game under coach Jason Garrett, installed after the midseason firing of Wade Phillips, Dallas was about to put the game away when, on third-and-6 from the Cowboys’ 42, the Saints forced and recovered a fumble at their own 11. The Saints then drove 89 yards for a score that ultimately gave them a 30-27 win.

The second of those occasions saw the Saints somehow survive a monster day from receiver Dez Bryant, who set a career high with 224 receiving yards on nine catches, two of which he turned into 58-yard touchdowns. New Orleans kicked a field goal in overtime to win 34-31, a bright spot in a 7-9 campaign marred by the bounty scandal and the season-long suspension for Payton that resulted from it.

Then there was the Saints’ clobbering at home of Dallas in Week 10 last year, when New Orleans set a league record with 40 first downs and a franchise mark for yards (625). New Orleanians relished the postgame interview in which befuddled Cowboys owner/General Manager Jerry Jones said it was “embarrassing” to lose in the fashion his team did and added, “I just didn’t expect this. I never saw this coming.” Compounding his embarrassment was the presence of Saints defensive coordinator Rob Ryan, who months earlier had been fired from the Cowboys by Jones.

Of course, Dallas can always point to its 24-17 victory in New Orleans in 2009 that snapped the franchise-best, 13-game winning streak with which the Saints opened the season. But that was relegated to a footnote when the Saints won the Super Bowl XLIV later that season.

Nonetheless, one day after practice this week, veteran Saints right tackle Zach Strief quickly noted that few of his teammates could take ownership of New Orleans’ record over Dallas since 2006.

Just five of today’s Saints were on the team that mauled the Cowboys in “Big D” in 2006: Brees, Strief, guard Jahri Evans, receiver Marques Colston and center Jonathan Goodwin (who is back with the Saints after a stint in San Francisco). Only eight were around for the showdown in 2009, 13 for 2010 and 15 for 2011.

“Can you put that up when in ’06 half your team was in college or in high school and say, ‘This is what happened. ... This is what our record has been?’ ” Strief said. “Probably not. They weren’t involved.”

Even the many players who were around for the 2013 blowout can anticipate grappling with a different kind of foe Sunday evening. Cowboys running back DeMarco Murray, who leads the NFL with 385 rushing yards and has punched in three touchdowns, has averaged 25 carries per game through three weeks. He only had that many rushes once in 2013. Meanwhile, the Cowboys defense in Week 3 had five starters in their front seven who did not start last year against the Saints.

Such factors were enough for Payton to emphasize all week that these Saints are 0-0 all-time against the Cowboys.

“This team hasn’t beat Dallas; last year’s team did,” Payton said. “There are a lot of new faces here and there as well.”