Marshawn Lynch ran for 131 yards, and Russell Wilson completed 15 of 26 passes for 187 yards and ran eight times for 67 yards for the Seahawks, who broke an eight-game postseason losing streak away from home.
Seattle will visit the top-seeded Atlanta Falcons next Sunday.
Lynch's 27-yard run with 7:08 remaining gave the Seahawks (12-5) the lead. On Washington's next series, Griffin reinjured the right knee he sprained about a month ago while trying to field a bad shotgun snap.
The knee buckled badly, and the Seahawks recovered the fumble and kicked an insurance field goal.
Kirk Cousins replaced Griffin, but Washington (10-7) was unable to come back.