Ahmad Bradshaw rushed for two touchdowns as New York (8-6) remained a game behind Dallas for the final NFC playoff spot.
The Redskins (4-10) were embarrassed by New York's defense, which recorded five sacks and picked off three Washington passes.
Manning completed 19-of-26 passes, connecting with Mario Manningham, Steve Smith and Derek Hagan for touchdowns, while Bradshaw carried the ball nine time for 61 yards.
The Redskins' Jason Campbell passed for 192 yards with a touchdown and two interceptions.
The Giants need wins in their final two games against Carolina and Minnesota and at least one Dallas loss to make the playoffs.