Austin caught 250 yards worth of passes in his previous outing against Kansas City, which earned him the first NFL start of his career. He justified Coach Wade Phillips' decision by running for 171 yards Sunday and also grabbing two of the three touchdown throws produced by Romo, who completed 21-of-29 for 311 yards.
For the second straight game and for the third time this year, Romo averaged more than 10 yards per passing attempt.
Atlanta drove 80 yards in 16 plays on the game's first possession and Matt Ryan hit Roddy White with a 4-yard scoring pass. It was all Dallas after that.
Romo completed a 59-yarder for a score to Austin that gave Dallas a 10-7 lead in the second quarter and then threw a 5-yard touchdown pass to Patrick Crayton with 6 seconds left in the first half.
Austin caught a 22-yard touchdown toss in the third period and Crayton, who fumbled a punt away against Kansas City two weeks ago, returned a punt 73 yards for a score in the final quarter. Nick Folk added three field goals for the Cowboys.
Ryan was 19-of-35 for 198 yards and two touchdowns and two interceptions.
Both teams are 4-2. Dallas has won two in a row and the Falcons had a two-game winning streak halted.
The 37 points for the Cowboys were the most they had scored since the second game of the 2008 season.