Vancouver was trailing 2-1 less than 3 minutes into the final period when Kesler tied the game, firing in the rebound of an initial shot by Sedin.
On the next shift, Sedin got control of the puck at the right point, circled into the high slot and unleashed a wrist shot that got past Washington's Michal Neuvirth for the decisive tally.
Zack Kassian also scored and Roberto Luongo improved to 14-1 lifetime against the Capitals with a 17-save performance as the Canucks reeled off a fourth straight win.
Neuvirth finished with 38 stops.
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