Joseph Randle had touchdown runs on the Cowboys' first two possessions for a quick lead, and none of Brandon Weeden's 14 pass attempts before halftime hit the ground; he had 13 completions and an interception.
But Matt Ryan threw two touchdowns to Julio Jones in the second half, fill-in running back Devonta Freeman ran for 141 yards with three scores against the NFL's top rushing defense as the Falcons overcame a trio of two-touchdown deficits for a 39-28 win Sunday.
"We couldn't keep our momentum that we built in the first half, carry over into the second half," said Weeden, who finished 22 of 26 for 232 yards.
Randle had a 28-yard run on the first play of the game, then after a penalty scored on a 37-yard run. He added 20 yards on his next play, but only 2 yards on his last 11 carries — including a 1-yard TD that made it 14-0.
"It felt like they had everybody in the box," said Randle, who emerged as the starting running back this season after the Cowboys lost NFL rushing leader DeMarco Murray in free agency.
The Cowboys had won their first two games, extending their regular-season winning streak to six games, even after Bryant broke a bone in his right foot in the opener and Romo sustained a broken left (non-throwing) collarbone last week at Philadelphia.
They still have the NFC East lead — Washington, Philadelphia and the New York Giants are all 1-2 — heading to winless New Orleans next week. New England visits Dallas in two weeks, but Bryant is likely out at least another month and Romo will miss another six games or more.
"Worried? No, not at all," Cowboys owner Jerry Jones said. "I wish we had all our players, but that's dreaming. I like what we did out there today. ... We just have a lot of work to do to stay in the hunt."
But Terrance Williams, the primary fill-in for Bryant, had only two passes thrown his way and didn't catch either.
With Romo watching with his left arm in a sling, Weeden started 9 of 9 to push his streak of completions to 16 to start the season.
Weeden's ill-advised throw while scrambling to his left was easily intercepted by William Moore, putting the Falcons on the Dallas 23. Freeman's second score pulled them within 21-14, though it was 28-17 at the half after Randle's third TD run and Matt Bryant's 32-yard field goal.
Ryan completed 24 of 36 passes for 285 yards, including a 45-yarder to Jones midway through the third quarter before a 2-point conversion that got the Falcons within 28-25. Jones caught 12 catches for 164 yards, his third consecutive 100-yard game to start the season.
Atlanta went ahead on Freeman's 7-yard run in the opening minute of the fourth quarter, and Jones caught a 2-yard TD with 3 minutes left.
"A lot of resolve to reset and come back and finish like we did," Falcons coach Dan Quinn said. "We clearly got punched in the mouth ... Dallas certainly had us reeling all the way through and we had to battle like crazy to get back in it."
Notes: The Cowboys played their 50th regular-season game at AT&T Stadium. They are 27-23 in the stadium that opened in 2009. ... Dallas' four rushing touchdowns in the first half were the most since at least 1991, according to the team.