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.
Swim Week Miami Beach 2014 [PHOTOS]