Pacioretty scored the winner for the Canadiens at 13:18 of the third, netting his 13th of the season by shooting the puck intro traffic in front of Smith's goal. The puck ricocheted off defenceman Michael Stone's skate and into the net.
Phoenix hasn't won in Montreal since 1996.
Boedker got the Coyotes on the board at 6:14 of the first period, banking his own rebound off his skate and into the net for his tenth goal of the year.
Price clearly wasn't expecting the puck to come back to him so quickly after the initial shot, and was out of position when it trickled past him. Former Hab Kyle Chipchura assisted on the goal.
The Coyotes outshot the Canadiens 15-3 in the first and had another 12 attempts blocked by Montreal players.
The Canadiens threatened the Phoenix net with more gusto in the second, but still couldn't put one past Smith. The home team came close to tying the game when Pacioretty fired a one-time shot off the crossbar late in the period.
The Canadiens finally found their equalizer to start the third. Markov scored his third of the year on the power play at 2:26, beating Smith between the legs with a slap shot from the point.
After Pacioretty made it 2-1, he added an empty-netter to seal the victory.
The win was Montreal's first when trailing after two periods (1-10-1).
Notes: Rene Bourque was in the lineup after missing the last seven games with a lower body injury. … Phoenix captain Shane Doan was absent (illness). … Smith entered the game with a .927 save percentage in six career games against the Habs. … Former Canadien Mike Ribeiro made his eighth career appearance versus Montreal since being traded in 2006. … The Coyotes' current road trip takes them to Toronto next. … The Canadiens and Coyotes meet once more this season on March 6, 2014, in Glendale, Arizona.