The Falcons (2-6) have had a penchant for squandering leads this season, coming into the game 1-3 when leading entering the fourth quarter.
Carolina was driving late, but Atlanta stalled the rally when Blidi Wreh-Wilson intercepted Teddy Bridgewater near the Falcons' 10-yard line with 1:04 remaining.
Moore on third and 18 to move the Panthers into Falcons territory.
Bridgewater was limited to 176 yards passing as the Panthers (3-5) lost their third straight game without injured Christian McCaffrey.
The Falcons avenged a 23-16 loss to Carolina 18 days ago in which Bridgewater threw for 313 yards and two scores and Mike Davis piled up 149 yards rushing.