Lindholm netted the game-winner with 5 1/2 minutes left in third as the Ducks extended a club record with a ninth straight win and wrapped up a 4-0 road trip.
Koivu and Cogliano each registered an assist and Jonas Hiller made 17 stops.
The game featured the return of Anaheim Coach Bruce Boudreau to Washington, where he served as head coach from 2007-11 before being fired.
Philipp Grubauer turned aside 26-of-29 shots.
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