Grossman completed 26-of-35 passes, racking up 314 yards, two touchdowns and two interceptions for the Redskins (4-7), who used the big play with 6:18 remaining to end a six-game skid.
Roy Helu added a touchdown en route to 108 rushing yards for Washington.
The Seahawks (4-7), meanwhile, lost despite two TD passes from Tarvaris Jackson, who compiled 144 passing yards on 14-of-30 efficiency.
Marshawn Lynch totaled 111 rushing yards on 24 carries and also caught a touchdown pass for Seattle.
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