Kansas City (10-3) can clinch a playoff berth with a win in any of their last three games.
Special teams played a big role as Dexter McCluster and Quintin Demps combined for 300 total return yards. McCluster's 177 punt return yards are a Chiefs' single-game record. He picked up 74 of them with a touchdown return early in the second quarter.
Demps racked up 123 kick return yards including a 95-yard touchdown return in the final minute of the first half.
The offense continued its upswing, punching in two touchdowns on the ground while adding two more through the air. Jamaal Charles ran for his first with 5:52 left in the first quarter to put the Chiefs on top 10-0.
Alex Smith connected with Dwayne Bowe for a 21-yard scoring strike to make t 17-0 before the end of the frame. Smith finished 14 for 20 for 137 yards and two scores.
Charles' second touchdown came on a five-yard pass from Smith and opened the scoring in the second frame. The running back finished with 151 yards rushing on 19 carries.
The defense stifled the Washington (3-10) offense, sacking Robert Griffin III six times despite still playing without linebacker Justin Houston.
Knile Davis picked up the only score of the second half with a 17-yard run to start the fourth quarter.