The Panthers broke the deadlock in the first quarter when Mike Tolbert bundled his way into the end zone to score from four yards.
Matt Bryant pulled the Falcons back into it with a field goal at the start of the second quarter, but the Panthers soon extended their lead when Cam Newton found Greg Olsen wide open on the edge of the end zone.
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Graham Gano restored the Panthers' seven-point lead early in the third quarter with a 55-yard field goal, and that advantage was doubled in the fourth when Newton scrambled to right side of the end zone from eight yards for a touchdown of his own.
The Panthers sealed the win on the very next drive as Drayton Florence intercepted Ryan's pass and returned it 38 yards to open up an 11-point lead. Gano added another field goal late in the quarter as the hosts eased to a comfortable victory.
The result leaves the Falcons still looking for their first away win of the season, while the Panthers stay second in the NFC South with a 5-3 record.