Nicklas Backstrom broke a tie early in the winner, as the Washington 3, at Verizon Center.
John Carlson and rookie Cody Eakin scored second-period goals for Washington, which avoided a fifth straight loss. Tomas Vokoun made 20 saves in the win, the 200th for head coach Bruce Boudreau.
Lauri Korpikoski had two goals for the Coyotes, who finished a five-game road trip with a 3-2-0 record. Jason LaBarbera stopped 27 shots in defeat.