Matt Ryan threw for 342 yards and no scores but was mistake-free as his running game and defense backed him up to hold off the visiting Cowboys (3-5).
"It sounds great," wide receiver Roddy White told reporters after becoming the Atlanta's all-time reception leader and being asked how it felt.
"It just speaks to consistency over the years."
White passed Terance Mathis with his fourth catch of the evening with 574 receptions as a Falcon.
"We're starting to beat good football teams," added White. "You need these kinds of wins so when you get in the playoffs in those tight games you can win."
With a seven-yard catch in the fourth quarter, Jason Witten became the Dallas's all-time leading receiver, though the record was to be merely a footnote in another tough loss.
Witten had seven catches for 51 yards, making it 754 for his career and surpassing Hall of Famer Michael Irvin, who had 750 catches from 1988-99.
After the teams exchanged a pair of field goals each in the first half, the Falcons took charge in the second when they got their running game moving.
Michael Turner, who rushed for 102 yards, scored a touchdown on a three-yard run early in the fourth, before Matt Bryant added his third field goal to give Atlanta a 16-6 advantage.
Tony Romo connected with receiver Kevin Ogletree for a 21-yard touchdown to pull Dallas within three with 5:21 left.
But the Falcons responded with a lengthy drive resulting in another Bryant field goal with just 17 seconds on the clock.
It was another heart-breaker for Dallas, who clawed back a 23-0 deficit last week against the New York Giants only to lose in the final minutes.
"We didn't do enough to win," said Cowboys coach Jason Garrett. "We have to find a way to make enough plays to win a game like this."
Romo threw for 321 yards but the team missed the presence of lead running back DeMarco Murray as he sat out a third straight game with a foot injury.
Atlanta, whose previous best start was 4-0, have a commanding four-game lead in the NFC South. Dallas have now lost four of five to fall 2-1/2 games behind first place in the NFC East.
Receiving duo White and Julio Jones again showed why they may be the best combo in the NFL.
Jones finished with five catches for 129 yards while White had seven for 118 to make it another strong day for Ryan.
"Two of the best players in the league," Ryan said of the pair. "These guys are special and I'm lucky to be around them."