McCoy carried the ball 31 times and ran for a score for the Eagles (1-0), who handed new head Coach Chip Kelly a victory in his first game along the Philadelphia sidelines.
Vick went 15-of-25 through the air for 203 yards with two TD passes and also rushed nine times for 56 yards and a score as the Eagles rolled up 443 yards of total offense.
DeSean Jackson led the Philadelphia receiving corps with seven grabs for 104 yards and a touchdown.
Robert Griffin III, playing in his first game since sustaining torn knee ligaments in last year's playoffs, completed 30-of-49 passes for 329 yards and two touchdowns but was also intercepted twice for the Redskins (0-1).
Exploding whale video goes viral on Internet
'SNL': 'Anchorman 2' cast, One Direction sing 'Afternoon Delight' [VIDEO]