In the second round, Desharnais snuck a low backhand between the pads of Ben Bishop. Carey Price then made stops on Jason Spezza and Daniel Alfredsson for the win.
Desharnais and Erik Cole scored in regulation for the Canadiens, who have won three of four. Price stopped 35 shots and all three shooters in the shootout.
Colin Greening and Erik Karlsson both had goals for the Senators, who have dropped their past two. Bishop finished the game with 24 stops.
Ottawa has 82 points and sits in the seventh spot in the Eastern Conference, but is just one point behind Boston for the lead in the Northeast Division and second, overall, in the conference.