Mike Comrie, Chris Kelly, Wade Redden and Jason Spezza also scored for the Senators (32-22-3), who moved three points over the reeling Canadiens (29-22-6) in the Eastern Conference standings.
Steve Begin scored in his return from a 27-game stint on the injured list with back spasms while Michael Ryder and Andrei Markov added goals for the Canadiens, who allowed the first goal for an eighth game in a row. They're 2-5-1 over that span.
Ray Emery made 37 saves for the Senators to get his 24th win of the season.
David Aebischer made 25 saves for Montreal to lose his second straight start.
Canadiens winger Sergei Samsonov made his return to the lineup after a three-game stint in coach Guy Carbonneau's doghouse, while Markov returned after missing the last three games with a strained knee.
Carbonneau benched winger Alex Kovalev for the first 17 minutes of the third period, while defenceman Janne Niinimaa didn't see the ice the entire third.
The Senators went ahead 5-2 with two quick strikes at the start of the third period, putting the game out of reach.
Alfredsson's wrist shot from the side boards went in off Fisher 17 seconds into the third, and Spezza one-timed a Dany Heatley feed off a 2-on-1 rush at 3:31 for his 22nd goal of the year.
Montreal cut the lead to 5-3 on the power play at 5:04 when Markov fired home a rebound.
Ottawa jumped out to a quick lead at 2:10 of the first when Comrie's slapshot from the left circle beat Aebischer through the legs for his 13th goal of the
season, and his sixth in 16 games as a Senator.
The Senators went ahead 2-0 when a loose puck jumped over Niinimaa's stick right to Comrie, whose shot went off the post but was banged in by Kelly at 10:26.
The second period featured lots of action with three goals and 11 penalties, including fighting majors for Chris Neil and Mike Komisarek just moments after they stepped out of the box.
Emery was also assessed a penalty in the second when he swung his stick and hit Canadiens forward Maxim Lapierre in the face, drawing a minor for slashing.
The Canadiens got to within one at 5:01 when Mike Johnson beat Emery to a dump-in behind the net and fed Begin in front.
Ryder tied it up for Montreal with a power play goal at 9:14, tipping home a Sheldon Souray point for his 16th of the year and his first in eight games.
The Sens regained the lead at 16:37 on a 4-on-3 power play, with Redden firing a perfect wrist shot top corner.
Notes: Canadiens D Craig Rivet missed his second game due to a bout of pneumonia. . . . The lone scratch for the Senators was winger Brian McGrattan. . . . Montreal scratched wingers Alexander Perezhogin, Aaron Downey and Garth Murray.