Price recorded his sixth career shutout, including a 19-save effort in a 3-0 win in Ottawa on Oct. 23.
"I really wanted to win this one and I think our guys knew it," said Price, who improved to 8-5-1. "My guys were helping me see the puck. They did a really good job of boxing out tonight. They did everything they could to help me. Everything I left out, they took care of."
Price turned aside 20 shots in the third, including 18 after Hamrlik's power-play goal put the Canadiens up by two at 4:39.
"He was unbelievable tonight," said Markov, who opened the scoring in the first. "He kept us in the game and he made a few unbelievable saves. It was a good team effort."
Roberto Luongo stopped 27 shots for Vancouver, which began a five-game road trip which continues Thursday night in Ottawa.
"It's always disappointing to lose, that's first and foremost," Luongo said. "It's the first game of our road trip and we really wanted to get off to a good start so it's going to be important to regroup [Wednesday], have a good practice and come ready to play against the Senators.
The Canucks had gone 6-0-1 since a 6-2 loss in Minnesota on Oct. 19. They had a seven-game winning streak from Jan. 16-30.
"They played a pretty solid game tonight," Price said. "I thought both teams played really well tonight, both offensively and defensively. Both teams were trying to create."
Markov gave the Canadiens a 1-0 lead with his first goal of the season at 6:53 of the first period. The veteran defenseman drove to the net to put home a loose puck after Luongo failed to cover up Brian Gionta's tip on a shot from the left corner by Tomas Plekanec.
Montreal was unable to convert each of its first three power-play opportunities, falling to 3-for-50 overall after failing to take advantage of Andrew Alberts' double minor for high sticking Mathieu Darche 2:21 into the second.
Hamrlik scored the Canadiens' fourth power-play goal of the season during their fourth man advantage of the game at 4:39 of the third.
With Alberts in the penalty box serving a delay of game penalty after his clearing attempt sailed over the glass, Hamrlik drove home a slap shot from the left side for his first goal.
Vancouver, which entered with a league-high 29.4 percent success rate on the power play, went 0-for-4 with the man advantage.
"The power play has been the difference for us the last few games," Canucks left winger Daniel Sedin said. "Tonight, we didn't do a good enough job."
Canucks coach Alain Vigneault fell short in his first bid for his 300th career win. Vigneault, who has 190 regular-season victories with Vancouver, got his first 109 wins with Montreal from 1997-2000. ... Canucks defenseman Dan Hamhuis returned after missing eight games because of a bruised foot. "For a guy who hadn't played in over three weeks I thought, in general there, he tried real hard and he's going to get better," Vigneault said. ... Canadiens coach Jacques Martin used his timeout prior to a faceoff in Montreal's zone with 1:24 remaining in the second.
Copyright by STATS LLC and The Associated Press
Arena: Bell Centre Location: Montreal, Quebec
Referees: Marc Joannette, Chris Lee Linesmen: Pierre Champoux, Anthony Sericolo
Attendance: 21,273 (100.0% full)
Team Stat Comparison
Power Play Goals
Power Play Opportunities
Shots on Goal
Andrei Markov (1)
Assists: Brian Gionta, Tomas Plekanec
No scoring this period
Roman Hamrlik (1)
(Power Play) Assists: Mike Cammalleri, Jaroslav Spacek