Newton scored on runs of 1 and 2 yards in the second half -- finishing with 52 rushing yards on 15 carries -- and went 18-of-28 through the air for 306 yards with no interceptions for Carolina (3-8).
The Panthers grabbed the lead for good on Graham Gano's 23-yard field goal with 12:43 left in the game and went on to record their second win in four contests.
Brandon LaFell and Gary Barnidge each made a scoring grab for the winners.
Rookie Nick Foles filled in for the injured Michael Vick and was limited to 119 yards on 16-of-21 efficiency for the Eagles (3-8), who dropped their seventh straight.
Bryce Brown subbed for running back LeSean McCoy (like Vick, out with a concussion) and piled up 178 rushing yards on 19 carries with two touchdowns in the loss.