Gionta supplied all of the Habs' offense, scoring twice in the second period to pull Montreal into a 2-2 tie and then finding the net on a backhander in the first round of the shootout.
Carey Price was perfect in the tiebreaker, turning away Washington's Nicklas Backstrom, Matt Hendricks and Alex Ovechkin.
Price stopped 27-of-29 shots for the game, including five in the overtime period, as Montreal improved to 4-1-2 in its last seven games.
Mathieu Perreault and Mike Knuble scored and Semyon Varlamov made 36 saves for the Capitals, who lost for the third straight time.
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