Gordon Gano connected on three field goals for the Redskins (5-9), who dented the Giants' playoff hopes with the surprising victory.
New York needed to best the Redskins to stay even with Dallas atop the NFC East, but instead lost for the fifth time in six games.
The Giants fell to 7-7, one full game behind the Cowboys, who beat Tampa Bay Saturday.
Eli Manning was intercepted three times in New York's setback.
The Giants will try to regroup Saturday against the Jets before taking on Dallas in the season finales for both teams on New Year's Day.
2014: NFL Cheerleaders [PHOTOS]
Michael Sam cut from the Dallas Cowboys