The win lefts the ‘Skins (5-6) into a first-place tie in the NFC East with New York (5-6).
Manning threw two interceptions in the first six minutes of the first quarter, and Washington dominated the second quarter, getting a Dustin Hopkins 41-yard field goal, a 63-yard touchdown pass from Cousins to DeSean Jackson and a 1-yard TD run by Cousins to go into the break up 17-0.
A 33-yard Hopkins field goal with 11:36 left in the fourth quarter pushed the lead to 20-0. Manning connected with Rueben Randle on a 40-yard TD pass at the 10:10 mark to get New York on the board.
Odell Beckham Jr. hauled in a 21-yard scoring pass with 4:57 left to get the Giants to within one score.
The Washington offense was able to run clock, getting a first down that enabled the Redskins to bleed 4:38 off the clock before punting the ball back to the Giants with 19 seconds left.
An effort at a hook and lateral on the final play of the game came up short.
Cousins was 20-for-29 passing for 302 yards and a touchdown. Alfred Morris ran for 78 yards on 23 carries.
Jordan Reed had eight catches on nine targets for 98 yards.
Beckham had a huge day receiving for New York, catching nine balls on 18 targets for 142 yards.
Manning was 26-for-51 passing for 321 yards, two touchdowns and three interceptions.
The Giants could only manage 33 yards rushing on 13 attempts.