The defending Super Bowl champion Giants appeared unstoppable in the early going, but sputtered during a scoreless second half while relying on their defense.
Washington barely reached the 200-yard mark in total offense and produced just 11 first downs.
Manning, who guided the Giants last season to the franchise's third Super Bowl triumph, drove New York 84 yards in 11 plays on its first possession and scored his team's lone touchdown on a one-yard run.
The next three New York possessions ended with field goals of 24, 25 and 47 yards by John Carney.
Having been outplayed throughout the half, the Redskins scored with 13 seconds left in the second quarter on a 12-yard throw from Jason Campbell to Santana Moss.
The teams combined for eight punts in the second half and Manning threw an interception. Washington ran out of downs at the New York 43 on its next-to-last possession and then ran out of time at the end of the game after moving to the Giants' 32.
Manning completed 19-of-35 passes for 216 yards. Ten of the completions went to Plaxico Burress for 133 yards and Brandon Jacobs picked up 116 yards on 21 carries.
Campbell was 15-of-27 for 133 yards.