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.
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