Ottawa jumped out to a 3-0 lead before the game was six minutes old, but then allowed the Canadiens to score seven straight times.
With already two on the night, Pacioretty completed his hat trick at 1:09 of the third and Desharnais made it 7-3 midway through the third beating Anderson up high.
The Senators finally managed to put an end to the onslaught 14 minutes into the third as Zibanejad beat Budaj.
Despite being outshot 15-4 in the second the Canadiens scored twice to take a 5-3 lead after 40 minutes.
Montreal took its first lead of the game as Eller jumped on a rebound early in the second to make it 4-3.
Ottawa appeared to tie it up on the ensuing play, but the goal was called back due to goaltender interference.
Montreal made it 5-3 on Pacioretty's second of the night as he took advantage of a Senators turnover and broke in alone to beat Anderson through the legs.
The game was made that much more interesting after Erik Karlsson checked Brendan Gallagher hard into the boards and Alex Galchenyuk took offense, leading to Karlsson and Galchenyuk exchanging a couple punches.
Trailing 3-0 the Canadiens got on the board as Markov scored off a bad angle down low on Montreal's second shot of the game. Two minutes later Weaver's point shot made it past a screened Anderson.
The comeback was completed as Pacioretty got past Ottawa's Eric Gryba on a bouncing puck and beat Anderson between the legs.
After giving up the early lead, Montreal's P.K. Subban saw just 37 seconds of ice time in the first and didn't get another shift until the Canadiens went on the power play at the two-minute mark of the second.
Ottawa opened the scoring at the two-minute mark of the first as Smith scored his first off his backhand.
The Senators made it 2-0 just over two minutes later as Hemsky tipped Patrick Wiercioch's point shot and it was 3-0 as Smith scored his second of the game off a great pass from Zibanejad.
The Senators played the third without Hemsky, who left with an upper body injury.
Ottawa next faces the Rangers Saturday night in New York, while the Canadiens return home to host the Detroit Red Wings.
Notes: C Jason Spezza returned to the Senators lineup after missing the last two games. The Senators were without D Jared Cowen (lower body, day-to-day), LW Colin Greening (lower body, day-to-day) and RW Bobby Ryan (sports hernia, out for season). LW Matt Kassian was a healthy scratch. The Senators used the last of its call-ups as it did the paperwork to change Jean-Gabriel Pageau's call-up from emergency to regular recall… Montreal D Douglas Murray served the first of his three-game suspension. RW Rene Bourque and D Nathan Beaulieu were a healthy scratch. RW Dale Weise missed the game with an upper body injury.