Atlanta (8-0) is the only undefeated team in the NFL. Dallas (3-5) is reeling, having lost four of five.
Michael Turner scored Atlanta's lone touchdown, a 3-yard run that gave the Falcons their first lead, 13-6, early in the fourth quarter. Four Matt Bryant field goals accounted for Atlanta's other points.
Romo tried to mount a fourth-quarter comeback. He hooked up with Kevin Ogletree on a 21-yard touchdown pass to cut the Falcons' lead to three with five minutes to play.
However, Atlanta converted three third downs on its ensuing drive and forced Dallas to burn all of its timeouts before Bryant nailed his fourth field goal with 17 seconds to play.
Roddy White caught seven passes for 118 yards and became the Falcons' all-time leader in receptions. Julio Jones also went over 100 yards receiving, as Matt Ryan threw for 342 yards. Ryan went 24-for-34 with no touchdowns and no interceptions.
Romo finished with 321 yards passing. He completed 25 of 35 with one touchdown and no interceptions.
In an even first half, neither team could find the end zone. Dallas made more big plays, with a 65-yard Kevin Ogletree reception and a spinning, 37-yard punt return by Dwayne Harris leading to two Dan Bailey field goals.
DeMarcus Ware blindsided Ryan on a second-quarter sack. The Cowboys held the Falcons to only 23 yards rushing in the first half.
Atlanta's defense came up with its own key moments before halftime. Cornerback Asante Samuel knocked away what looked like a certain touchdown catch by Dez Bryant, and the Falcons forced Dallas to settle for field goals on two drives inside the 20-yard line. The Cowboys had only 25 yards on the ground.
The Falcons held on a third-and-1 at midfield late in the first half, then took over at their own 12-yard line after a punt. Atlanta capitalized with a last-minute drive that culminated in a 46-yard Matt Bryant field goal that tied the game 6-6 at halftime.
Bryant also made a 45-yarder early in the second quarter, but he missed a 37-yard attempt in the first quarter.
The Cowboys play the Eagles in Philadelphia next week, while the Falcons head to New Orleans for their first shot at the Saints this season.
NOTES: White's fourth catch of the game was the 574th of his career, passing the franchise record held by Terance Mathis, who played for Atlanta from 1994-2001. ... Falcons linebacker Sean Witherspoon was inactive. Mike Peterson started in his place. ... Cowboys running back DeMarco Murray missed his third consecutive game with a sprained foot. Felix Jones started in his place. ... Romo's record in November fell to 19-3 with the loss. ... Falcons defensive end Peria Jerry left in the first half with a knee injury. ... NFL commissioner Roger Goodell was in attendance. ... The Falcons distributed 70,840 tickets for the game.