Kirk Cousins threw this second touchdown of the day, giving the Falcons a 14-3 lead over the Cowboys with 8:28 left in the first half.
The Cowboys are in danger of being blown out again, with the Falcons outgaining them 169 to 89.
The Falcons went for it on fourth-and-three, and with three receivers lined up on the right, Cowboys cornerback Trevon Diggs got caught in the wash. He ran into the back of Falcons receiver KhaDarel Hodge.
Mooney has three catches for 68 yards, and Drake London two for 27. London caught a 9-yard touchdown pass from Cousins with 5:23 left in the first quarter.
Cousins is 12-of-13 for 134 yards.