The Cardinals took a 7-0 lead on the Falcons, but it lasted only 2:14.
Arizona running back David Johnson had a 1-yard touchdown run, capping an eight-play, 64-yard drive.
The Falcons had only one first down, 4 yards and punted twice on their first two possessions, but they tied the game with help from their defense.
Josh Rosen threw a pass intended for Johnson that Vic Beasley tipped in the air. Deion Jones intercepted the batted ball and ran 41 yards to the end zone to tie the game 7-7.
It was the fourth pick-six Rosen has thrown this season.
The rookie now is 3-for-6 for 63 yards and the interception.