Andrei Markov, Mike Weaver, Lars Eller and David Desharnais also scored for Montreal, which trailed 3-0 less than 6 minutes into the game. Peter Budaj stopped 39 shots for his 10th win of the season for the Canadiens.
Pacioretty completed his hat trick at 1:09 of the third and Desharnais made it 7-3 midway through the final period by beating Anderson up high.
The Senators got on the board again with 5:53 remaining 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 disallowed 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 of 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.
Pacioretty got the tying goal as he 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.
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. ... Ottawa 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 healthy scratches for the Canadiens, and RW Dale Weise missed the game with an upper body injury.