Washington returned the second-half kickoff 101 yards for a score and then broke a 20-20 tie with a 99-yard kick return with 6:24 to go.
Washington became the 10th player to return two kickoffs for TDs in game. It happened twice last year: Ted Ginn of Miami against the New York Jets on Nov. 1; and Josh Cribbs of Cleveland against Kansas City on Dec. 20.
The former Jets player missed most of last season with a broken right leg. He was acquired by the Seahawks for a fifth-round pick in the April draft.
Washington finished with 253 yards on kickoff returns, nearly matching Seattle's total offensive output of 271 yards. He's now tied for second all-time with six career kickoff returns for scores.
"When I get into the meeting tomorrow, trust me, all the guys in front of me will get the glory. On the first one I didn't even get touched. On the second one I barely got touched," Washington said. "You've got guys that hold on to their blocks as long as they did and working hard, you've got to be so thankful."