Foles completed 17-of-26 passes and ran for a touchdown while McCoy carried the ball 20 times for 77 yards as the Eagles (6-5) built up a 20-0 lead.
They had to turn back a fourth-quarter Redskins surge, however, before notching the victory, which snapped a 10-game home skid and gave them first place in the NFC East.
Robert Griffin III tossed a 62-yard TD pass to Darrel Young and a 41-yarder to Aldrick Robinson during the fourth quarter comeback for Washington (3-7).
He got the Redskins to the Eagles 18-yard line on the game's final drive, but was hurried on third down and tossed an interception to Brandon Boykin.
Griffin threw for 264 yards on 17-of-35 passing with two touchdowns and the game-ending interception.