Price, who also won the Ted Lindsay Award as the players' choice for the most outstanding player and Hart Trophy as most valuable player, picked up 27 of 30 first-place votes from the NHL's general managers.
"I have to really thank everybody who did vote for me," Price said. "I guess for whoever didn't vote for me, I'll try harder next year."
Pekka Rinne of the Nashville Predators finished second and Devan Dubnyk of the Minnesota Wild third. Rinne, Dubnyk and the New York Rangers' Henrik Lundqvist each picked up a first-place vote.
Price was by far the biggest reason the Canadiens finished first in the Atlantic Division. The 27-year-old went 44-16-6 with a league-best 1.96 goals-against average and .933 save percentage.
He called the franchise-record 44 victories his biggest accomplishment.
"That's something I can share with my teammates," Price said. "That stat right there just shows how good of a team we had. That one is 100 per cent it."
Price finished just behind Marc-Andre Fleury of the Pittsburgh Penguins for the lead in shutouts, as he recorded nine in 66 games.
The Vezina Trophy in Price's eighth NHL season was evidence of his absurdly good season. After winning that, the Hart and Lindsay, he reflected on his time in Montreal and getting to this point.
"I really got to thank the organization for not giving up on me," Price said. "I had a learning curve to go through. Fortunately they saw that I had the personality to get through it."
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