Jason Spezza, Mike Comrie and Dany Heatley also scored for the Senators (46-24-8). Ray Emery, playing in his 100th career game, stopped 26 shots. Sheldon Souray and Mark Streit scored for the Canadiens (40-32-6). Jaroslav Halak faced 37 shots.
Fisher opened the scoring five minutes into the first period as he beat Halak to the glove side.
Spezza made it 2-0 less than two minutes later as his wrist shot caught Halak by surprise.
The Canadiens made it 2-1 as Souray scored a power-play goal from the point, but with less than two minutes remaining in the period Comrie put Ottawa ahead 3-1.
The Canadiens finished the last 64 seconds of the period with a two-man advantage and had 56 seconds remaining on the power play at the start of the second, but were unable to take advantage.
Montreal had a four-minute power play late in the second after Dany Heatley cut Souray with a high stick. But once again the Senators were able to hold off the Canadiens.
Montreal finished the game 1-for-6 with the man advantage, while Ottawa was 0-for-2.
With his 10th of the season Streit brought the Canadiens to within a goal after scoring on a great pass from Maxim Lapierre.
Both Emery and Halak were solid in the third, giving the sellout crowd of 20,185 at Scotiabank Place plenty to cheer about.
Fisher added some insurance late in the third with his second goal of the night. Heatley picked up his 47th of the season into the empty net to round out the scoring.
Friday's game was the last between the two teams, with Ottawa winning the season series 5-3.
Notes: Ottawa LW Dean McAmmond played in his 800th career game . . . Ottawa was without RW Patrick Eaves (lower body injury, day-to-day) while D Lawrence Nycholat and RW Brian McGrattan were healthy scratches . . . The Canadiens were without G Cristobal Huet (hamstring, day-to-day) and RW Alex Perezhogin (concussion, day-to-day) while G Michael Leighton, LW Sergei Samsonov, LW Garth Murray and D Josh Gorges were all healthy scratches.