Mike Tolbert completed a 72 yard drive when he ran two yards into the endzone after 05:36.
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Celeb Sturgis pulled three points back after 09:18 of the second quarter when he kicked a 52-yard field goal.
Cam Newton then ran a touchdown to complete a 60-yard drive and extend the Panthers' lead.
Sturgis then added three more points from 29 yards with four seconds remaining in the first half as the Eagles closed the gap to 14-6 at half time.
Tolbert scored his second touchdown of the night 03:10 into the third quarter when he caught a pass from Newton.
The play of the game came two minutes later when Ryan Mathews silenced the Carolina crowd by spinning past the defence to run for 63 yards and score the Eagles' first touchdown.
Sturgis scored another field goal on 09:12 to bring Eagles to within five points, but Graham Gano cancelled it out with a field goal of his own at the start of the fourth quarter.
Luke Kuechly thought he had forced the Eagles into a punt with 2:47 left on the clock, but a flag on the play saw the ball pulled back.
The Eagles were unable to make the first down regardless, and turned the ball over on the 16-yard line. Carolina made them pay as Gano kicked a field goal with 23 seconds left on the clock.