The New Orleans Saints’ defense, which allowed a league-high 491 yards per game, allowed a record-setting dog barking sound to ring out from the Cowboys’ stadium.
A pair of penalties by defensive end Chris Jones also led to fumbles and touchdowns.
The Saints also dropped a touchdown pass on a fake punt.
The teams traded touchdowns on the next two drives to cut the deficit to 27-20 with 3:38 remaining.
The Cowboys were the first team in the NFL to lose consecutive games.
Dallas had won six straight.
“We came out with the same plan,” coach Jason Garrett said.
“It was about the same scheme, same mentality.
We were out-coached and out-battled.
We couldn’t get anything done.
We got the ball back to the defense, and we didn’t stop.”
Dez Bryant, who had 11 catches for 133 yards and two touchdowns, scored on a 23-yard reception with 5:33 remaining.
He caught a 10-yard touchdown pass from Jones to Brandon Coleman with 3 minutes, 33 seconds remaining in the fourth quarter to cut Dallas’ lead to 31-26.
Bryant ran for the touchdown, but the Cowboys held on for a 28-26 win.
“I thought we were the better team,” Jones said.
The first three quarters were spent mostly on defense, when the Saints led by a touchdown three times.
That changed with a pair of late turnovers and a fumble by defensive tackle Jairus Byrd.
The second was Jones’ pick six with 2:45 remaining.
“You know, I had a pretty good game,” Jones told reporters.
“They were on the run a little bit, but I think it was just the game, man.
They made some plays, and that’s the way it goes.”
After a field goal by Jones with 11:53 remaining, Bryant’s 11-yard TD pass to Coleman was blocked by Cowboys safety Lance Briggs.
Bryant’s TD pass gave Dallas a 36-31 lead with 4:21 remaining.
Cowboys safety Mike Jenkins returned the ensuing kickoff 63 yards for a touchdown to make it 38-34.
It was the first lead the Cowboys could secure in a half.
“There were no points and we just kept playing the same,” Jones, who missed his third straight game, said.
With Jones, the Saints had an early 3-0 lead, but Bryant’s field goal made it 35-32.
The game ended when defensive tackle DeMarcus Lawrence knocked a punt off the end zone with 1:05 remaining in regulation.
Jones finished with three catches for 37 yards.
“Just keep playing, keep making plays, keep putting yourself in good positions,” Jones added.
Bryant and Coleman, who combined for 11 tackles, combined for 16 quarterback hits.
Bryant had a sack, including an 11-pounder, and a forced fumble.
Bryant said he’s proud of his teammates.
“Everybody’s playing so well, and I’m proud of everybody,” Bryant said.
Coach Sean Payton, whose team is coming off a win against the Chicago Bears, said he had a good talk with Bryant and his teammates after the game.
“My message to the guys was that I know they’ve been playing for me,” Payton said.
He didn’t give an exact time frame for the game but said he expects it to be “pretty close.”
“We’ll get to the bye week, and then we’ll get back to practice.
I think we’re going to be in the best shape that we can be.”
Cowboys owner Jerry Jones and general manager Mark Dominik also didn’t say when the Cowboys will start practicing.
“This is a big win for us, and our focus will remain on winning football games,” Dominik said.
Bryant, the NFL’s leading rusher with 1,076 yards, added 109 receiving yards.
Coleman added 107 yards on seven catches.