Griffin, still feeling the effects of a sprained knee ligament that forced him to miss last week's game, played with a brace on his knee but still managed to amass 198 passing yards with an interception on 16-of-24 attempts.
Washington held on for the victory when a late comeback try by the Eagles fell short as Nick Foles was penalized for intentional grounding with 1 second left at the Redskins' 5-yard line.
With its sixth straight win, Washington (9-5) now can clinch the NFC East title with a victory next week over Dallas.
Alfred Morris gained 91 yards and scored a touchdown on 22 carries for the Redskins.
Philadelphia (4-11) meanwhile, lost for the ninth time in 10 games.