IRVING, Tex. — After six straight losses, the Atlanta Falcons were due for a couple of breaks.
Safety Robert Moore recovered two Dallas fumbles that the Falcons turned into touchdowns in a 21-10 victory, Atlanta's first win since the strike ended.
"Thanks, Dallas," Moore said. "The ball just kept finding me. It was unreal."
Atlanta (3-9) scored first-quarter touchdowns in a span of 13 seconds for a 14-0 lead. Scott Campbell hit Floyd Dixon with a 28-yard scoring pass and, on the ensuing kickoff, Moore picked up a fumble by Kelvin Martin at the Dallas 20 and ran for his first NFL touchdown.
The Cowboys (5-7), one defeat away from a second straight losing season after going 20 years without one, got back into the game on Roger Ruzek's 44-yard field goal and Herschel Walker's 1-yard run.
But Moore recovered another Dallas fumble at the Cowboys' 45 and Campbell scored on a one-yard plunge to give Atlanta a 21-10 lead early in the third quarter.
The Falcons, who had given up more points than any team in the league, blanked the Cowboys in the second half.
"Let's hope this is a start," Atlanta Coach Marion Campbell said. "We just had to have this game."
Gerald Riggs, who rushed 30 times for 119 yards, became the Falcons' all-time rushing leader with 6,023 yards, passing William Andrews.
Riggs said winning was enough.
"You don't know what it's like when you are losing," he said. "You don't know what it's like going in your own house and some people don't want to see you. It's been darn tough."
Dallas quarterback Steve Pelluer, who threw two interceptions, was replaced at quarterback in the fourth period by Danny White.
White moved the Cowboys to the Falcons' nine-yard line with 2:29 left but Dallas ran out of downs. The Cowboys got the ball back, but White's pass was intercepted by James Britt with 1:22 remaining at the Atlanta 10.
The crowd of 40,103 was the Cowboys' smallest home attendance since 38,499 watched them play at the Cotton Bowl in 1965.
"This is as low as we can get," Coach Tom Landry said after the Cowboys' playoff hopes all but disappeared. "We have to win them all and everybody has to lose or we are out."