Lawrence Tynes started the scoring with a 28-yard field goal, his first of three in the game.
Manning, who was 20-of-29 for 256 yards, connected with Mario Manningham on a 30-yard touchdown and Osi Umenyiora returned a fumble 37 yards for a score.
Ahmad Bradshaw rushed 12 times for 60 yards for the Giants (1-0).
Jason Campbell completed 19-of-26 passes, one of them a 17-yard touchdown strike to Chris Cooley, for Washington (0-1).
The Redskins also got an 8-yard touchdown run from Hunter Smith and a 27-yard field goal by Shaun Suisham.