Brown, a rookie who had never even started in college, lit up the Panthers for 178 yards rushing and two touchdowns but it was not enough to avoid a seventh successive Eagles defeat.
Both NFC teams have disappointing 3-8 records.
Carolina trailed 22-21 in the third before one of Philadelphia's three lost fumbles set up a go-ahead field goal by kicker Graham Gano.
Cam Newton took over from there, capping a 60-yard drive in the fourth quarter with a two-yard running score for the winning margin.
Newton had a rare banner day in a tough season as the second-year quarterback finished with 306 yards passing, two scores in the air and another two on the ground.
The Eagles played without concussed starters Michael Vick and LeSean McCoy, which opened the door for Brown who provided highlights in yet another Philadelphia (3-8) loss.