Tuck became the first Giants player with four sacks in game since Osi Umenyiora recorded six against Philadelphia in 2007 as New York (5-7) racked up its fifth win in six games.
Eli Manning completed 22-of-28 passes for 235 yards with a touchdown and an interception.
Brandon Myers led the Giants' receiving corps with five catches for 61 yards and a score.
Robert Griffin III compiled 207 aerial yards with a touchdown and ran for 88 yards for the Redskins (3-9), who dropped a fourth straight.
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