The Seahawks led 17-7 in the fourth quarter before a 28-yard run by Washington's Ray Helu made it 17-14. Then they went ahead with 6:18 left on a 50-yard touchdown pass from Grossman to Anthony Armstrong.
Grossman finished with 314 yards, two touchdowns and two interceptions on 26- of-35 passing, while Roy Helu had a nice day on the ground, rushing for 108 yards and a score for the Redskins (4-7), who snapped a six-game losing streak.
Tarvaris Jackson threw for 144 yards, two touchdowns and one interception on 14-of-30 passing, while Marshawn Lynch ran for 111 yards on 24 carries for the Seahawks (4-7), who had their two-game winning streak halted.
Red Bryant blocked a field goal and an extra point for the Seahawks, and kicker Steven Hauschka made one of two field goals. Receiver Sidney Rice suffered a head injury and was forced to leave the game early.