The game-winner was a 75-yard catch-and-run from Matt Ryan with 4:17 left. The signal-caller overcame a slow start and tossed for 318 yards and four touchdowns on 22-of-38 attempts for the Falcons (8-5).
After falling behind 23-7 late in the first half, Atlanta reeled off the next 24 points and remained in contention to claim an NFC wild card spot.
Roddy White made seven catches for 82 yards and a score for the victors.
Cam Newton started well for Carolina (4-9) but then came unraveled, finishing with 276 yards, two touchdowns and a pair of interceptions on 19-of-39 efficiency.