The Falcons then worked the clock, holding the ball for 5 minutes, 4 seconds, leaving only 17 seconds after Bryant's 32-yard field goal.
The Cowboys burned all their timeouts as Ryan kept the Falcons' offense on the field in the crucial time-consuming drive. Ryan passed to Jacquizz Rodgers for 31 yards and 11 yards on third-down plays. A defensive holding call against cornerback Orlando Scandrick on another third down prolonged the possession.
Finally, the Cowboys stopped Turner on a third-down run at the Dallas 14.
Romo never attempted a deep pass, though he had only 17 seconds to cover 80 yards. He found Jason Witten for passes of 7 and 11 yards, leaving 9 seconds. He passed to Felix Jones for 8 yards, leaving time for one play from the Cowboys 40.
Romo scrambled before passing to Jones, who was dropped near the Atlanta 22 to end the game.
"I think any time you're in that situation you obviously want to get the ball back with a chance, and it's tough," Romo said. "That's why they're a good football team. They're tough to beat at home. They proved it when they were able to run the clock out at the end."
Ryan was 24 for 34. Roddy White had seven catches for 118 yards and passed Terance Mathis for the most receptions in Falcons history. Julio Jones had five catches for 129 yards.
There also is a new Dallas leader for career receptions. With seven catches for 51 yards, Witten has 754 for his career, passing Michael Irvin's record of 750.
Miles Austin led the Cowboys with seven catches for 76 yards.
Cowboys owner Jerry Jones said he was "extremely, extremely" disappointed.
"We certainly didn't plan to end up here at 3-5 halfway through the season," Jones said. "We've got some tough ballgames. We've got half our season left."