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 said 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."
Indianapolis quarterback Andrew Luck set a new single-game rookie passing record while Peyton Manning and Aaron Rodgers both led their respective teams to impressive wins.
Luck threw 433 yards in his team's 23-20 win over the Miami Dolphins, eclipsing the previous rookie record of 422 set by Cam Newton last season.
The Pittsburgh Steelers upset the New York Giants with a 24-20 win at MetLife stadium, two fourth quarter touchdowns sealing a win for Mike Tomlin's team on a tough day for Eli Manning and the Giants offense.
Aaron Rodgers threw four touchdowns for the Green Bay Packers in their 31-17 win over the Arizona Cardinals, who suffered a fifth straight defeat.
Peyton Manning recovered after throwing two interceptions to lead the Denver Broncos to a 31-23 win at the Cincinnati Bengals while the Baltimore Ravens beat the Cleveland Browns 25-15 after giving up a 14-point lead.
Luck, last season's number one draft after graduating from Stanford, completed 30 of 48 passes as the Colts improved to 5-3.
After a Dolphins field goal, Luck got Indianapolis on the scoreboard via a route that was very well used by his predecessor Manning, a nine yard touchdown pass to receiver Reggie Wayne.
The Dolphins' own rookie quarterback Ryan Tannehill came into the league with much less fanfare than Luck but showed his quality with a 31 yard pass to Charles Clay for a touchdown.
After a Colts field goal, Miami got back in front thanks to a weaving 18 yard touchdown run from Reggie Bush.
In the third quarter, Luck hurled a 36 yard pass into the end-zone to T.Y Hilton, who made a magnificent catch despite double coverage to put the Colts back ahead.
The two teams exchanged field goals in the fourth quarter but Miami (4-4), blew a chance to win the game when Sean Smith dropped an attempted interception inside the Colts 30 yard line with less than four minutes left.
The victory was the third in a row for a Colts team who were watched by their head coach Chuck Pagano, who has been undergoing treatment for leukemia.
The Green Bay Packers (6-3) offense is firing again, they put up 176 yards on the ground while quarterback Rodgers threw for 218 yards and four touchdowns, including two to Randall Cobb.
Rodgers wrapped up a convincing performance with a 72 yard pass down the middle to Tom Crabtree.
The Giants managed just 182 yards of total offense against the Steelers but were in a strong position leading 20-10 at the end of the third quarter.
Mike Wallace's superb catch and pacy run for a 51-yard touchdown cut the Giants' lead to 20-17 just 55 seconds into the final quarter.
After squandering a sure three points with a fake field goal on a fourth-and-one from the New York three-yard line, Isaac Redman, the Steelers' third-string running back powered into the end-zone from a yard out to win the game.
Baltimore needed a 19 yard touchdown pass from quarterback Joe Flacco to Torrey Smith and then a 43 yard Justin Tucker field goal to get their 10 point win over the Browns whose 15 points all came from the feet of kicker Phil Dawson.
The Washington Redskins suffered a 13-21 home defeat to the Carolina Panthers and if you believe the 'Redskins Rule' that could be good news for Republican candidate Mitt Romney in Tuesday's presidential election.
Since 1940, with just one exception, George W. Bush's win over John Kerry in 2004, a Redskins win in their final home game before a presidential vote has meant victory for the incumbent with a loss meaning a triumph for the challenger.
The Panthers ended a five-game losing streak with quarterback Newton throwing for 201 yards and a touchdown.
The Houston Texans moved to 7-1 with a 21-9 win at Buffalo, Arian Foster ran for 111 yards and quarterback Matt Schaub threw two touchdown passes.
Manning threw two interceptions that led to his Broncos (5-3 trailing 20-17 to the Bengals.
But for the 38th time in his career, Manning led a fourth quarter comeback with crucial drives ending with touchdown passes to tight-end Joel Dreessen and Eric Decker, the latter after an interception by Champ Bailey.