Backstrom provided a goal and an assist during regulation while Alex Ovechkin played a key role with scores in regulation and the shootout for the Caps.
Holtby finished with 30 saves as Washington compiled a third straight win.
Arron Asham returned from a injury absence with a tally for struggling New York, which fell for the fifth time in seven games. Derek Stepan scored and Lundqvist turned aside 22 shots.
Aaron Carter is still in love with Hilary Duff
Millions of Getty images now available for free via embed tool