Dallas linebacker Anthony Dickerson trapped New Orleans quarterback Ken Stabler in the end zone for a safety with 1:58 to play today, turning what appeared to be a Saints' victory into a 21-20 victory for the Cowboys.
"I don't know what happened out there," said Dallas Coach Tom Landry. "I don't understand it.
"We just have to thank our defense. They made the big plays when they had to.
"It's nice to have big plays going for you and we have had them this year. But it's also nice to be able to make consistent, long drives and we haven't done that."
Asked if his team was motivated, Landry replied, "I hope not. If we were motivated and played that bad, we're pretty poor."
The safety came after the Saints had claimed six turnovers in the second half and had sacked Dallas quarterback Danny White seven times.
Tyrone Young had also blocked an extra point attempt by Dallas' Rafael Septien with 7:05 to play.
The Saints, clinging to their 20-19 lead, produced their sixth turnover on an interception by linebacker Dennis Winston at the New Orleans goal line with just over two minutes to play.
But on second and five from his 10-yard line, Stabler surprisingly went back to pass. Even more surprisingly, the Cowboys called a blitz on the play.
Dickerson, charging in from the right side of the Cowboys' defense, had a clear shot at Stabler and dragged him down two yards deep in the end zone.
Saints Coach Bum Phillips said, "Dallas was Dallas. We thought we had them at the end.
"We were passing down there because if we just ran three plays and punted, then a field goal would have beaten us anyway."
Dickerson said he wasn't surprised New Orleans passed from the end zone.
"I got up early this morning and watched the game of the week on television and saw the Saints did the same thing last week against the Green Bay Packers," Dickerson said.
The remarkable Dallas escape began with the Cowboys scoring 10 quick points on a four-yard throw from White to Drew Pearson and a 41-yard field goal by Septien.
New Orleans tied the game on a 19-yard field goal by Morten Andersen and a two-yard run by Wayne Wilson before Septien's 34-yard field goal gave the Cowboys a 13-10 halftime lead.
But as the second half began, the Cowboys began to self destruct. White was intercepted three times, flanker Drew Pearson was intercepted when he tried to throw on a trick play, Dallas fumbled a punt and also fumbled away a kickoff return.
White said, "Every year Bum Phillips comes up with something new and they blitzed us and blitzed us. They sacked us seven times because we couldn't pick it up."
New Orleans could score just 10 second-half points on a two-yard field goal by Andersen and a one-yard run by Wilson.
Dallas' final touchdown came with 7:05 to play as the Saints were trying to assume a 10-point advantage. Ed Jones broke through to block a field goal attempt by Andersen, Ron Fellows picked the ball up and ran 62 yards for a score.
But it was after that touchdown that Septien had his string of 88 consecutive extra point conversions come to a halt with Young's block.
White experienced a tough afternoon, completing 15 of 30 passes for 166 yards with three interceptions. He was sacked for 56 yards in losses and the Cowboys netted just 99 total passing yards.
Stabler completed 18 of 34 passes for 210 yards against the Dallas defense, which sacked him three times.
It was New Orleans' 10th loss in 11 games against Dallas. The Saints were trying to beat the Cowboys for the first time since 1971.
Dallas running back Tony Dorsett became the ninth leading rusher in NFL history when he gained 124 yards on 16 carries to pass Leroy Kelley.
Cowboys backup middle linebacker Scott McLean, a rookie from Florida State, suffered torn knee ligaments during the game and a club spokesman said surgery would be performed tonight.