Roman Hamrlik, Tomas Plekanec, and Andrei Kostitsyn scored for Montreal, which has won both matchups so far this season with its Original Six rival. James Wisniewski added a pair of assists in the victory, the Canadiens’ fourth in their last five games.
Henrik Lundqvist made 38 saves in defeat.
After a scoreless second period, the Rangers cut the lead to 3-2 with 13 minutes left in the game.
Derek Stepan found Zuccarello at the right doorstep and after his initial shot was denied, the Norwegian rookie sent the rebound top shelf, far side over Price.
Brian Boyle’s bid for a second goal midway through the period rang off the crossbar and Price stopped Stepan from the right circle with four minutes left.
The Rangers pulled Lundqvist with 1 1/2 minutes left and grabbed a two-man advantage when Hal Gill went off for hooking with 65 ticks to go.
Price made a save on a Boyle backhander from the slot with 20.8 seconds left and then again from the right circle in the final seconds to preserve the win.
“They had a strong third, they came to work but our guys did the job of holding them off,” Price said. “We sat back a little bit, but got the job done.”
Boyle pushed the puck past Price from the right door step during a goal mouth scramble to give the Rangers the lead seven minutes into the contest.
The Canadiens took advantage of two power play opportunities and then added an even strength marker in a span of 2:47 late in the first period to generate all the offense they would need to win the game.
The hosts tied the game when Hamrlik ripped a drive from the top of the left circle past Lundqvist and then took the lead 1 1/2 minutes later.
P.K. Subban faked a shot from the left point and sent a cross ice pass to Plekanec, who stopped it with his skate and then buried a wrister into the open cage to put the home team ahead for good with 5:10 to go in the period.
Jeff Halpern fed from behind the net into the slot for Kostitsyn, who whistled a slapper past Lundqvist to end a nine-game goal drought with 3:57 left in the stanza.
“After the first two, as a whole, we were slow on the puck,” Rangers coach John Tortorella said. “It took us a couple of periods to get going. They’re a quick team. We never got near the puck. We were just that slow. But in the third we got our legs underneath us and got to the game we needed to play. That’s chip-em, grind and try to hold the neutral zone.”
Kostitsyn notched his 78th career goal to tie Keith Acton, Bud O’Connor, Brian Skrudland and Marc Tardif for 77th place on the Canadiens all-time list…He also registered his 165th career point to tie Edouard “Newsy” Lalonde for 88th on the all-time franchise list…Plekanec recorded his 117th goal to move into a tie with Claude Larose and Doug Risebrough for 44th place on the team’s all- time leaderboard…Price beat the Rangers for a second time in five meetings to earn his 82nd career win, good for a tie with Wilf Cude for 13th on the Canadiens all-time list…while Lundqvist is 10-8-2 in 21 matchups against Montreal…Dan Girardi had a pair of assists in defeat.