Griffin, who went No. 2 in this year's NFL draft after the Colts chose Andrew Luck, played into the third quarter, guiding the Redskins on two touchdown drives.
Rex Grossman also played behind center for Washington, completing all eight of his pass attempts for 127 yards and two scores.
Redskins Rookie running back Alfred Morris carried the ball 14 times for 107 yards and a touchdown.
Luck, meanwhile, also stayed in until the third quarter, completing 14-of-23 passes for 151 yards and a touchdown.