The score, with 6:06 remaining, pushed the Seahawks to a one-touchdown lead and they struck again 28 seconds later when Marcus Trufant picked off a pass and ran 78 yards for another TD.
Seattle then added another score near the end of the game.
Hasselbeck passed for 229 yards with a touchdown and two interceptions.
Washington's Todd Collins had similar numbers, passing for 266 yards, two touchdowns and a pair of interceptions.
Seattle (11-6) advanced past the first round of the playoffs for the third year in a row.
Washington finished with a record of 9-8.