Pacioretty took a short feed in front from David Desharnais and shoved a shot past Evgeni Nabokov for his 12th goal. Nabokov stopped 24 shots and was the hard-luck loser as he came back from injury.
It was Price's second shutout this season for the Canadiens, who snapped a two-game skid and improved to 10-2-1 in their last 13. They have scored only two goals in the past three games.
Montreal spoiled the NHL debut of prized Islanders prospect Ryan Strome, the No. 5 pick in the 2011 NHL draft.
New York (9-19-6) returned from a 1-4 trip and lost for the 12th time in 13 games (1-9-3). The Islanders are 0-16-4 when they score fewer than three goals.
However, they appeared to get a jolt in the third period when Lars Eller levelled New York captain John Tavares as he carried the puck behind his net and back out the right side. Tavares didn't seem to see Eller charge at him and wasn't injured.
Eller was given a minor penalty for illegal contact to the head, but the Islanders' anemic power play did nothing with the advantage.
The 38-year-old Nabokov returned after missing 11 games because of a groin injury sustained against Detroit on Nov. 16, the last time New York won at home.
The teams played a fairly even first period, with Montreal holding an 11-9 edge in shots, but the Islanders came closer to breaking the scoreless deadlock. Tavares had the best chance when his shot slipped between Price's pads, slid through the crease and struck the right post with 6:45 left.
The second period provided little more action than the opening frame, and the teams headed into the final period of regulation still deadlocked.
Both teams received their first two power plays of the game, yet couldn't do much with them. Montreal entered with the NHL's best power play on the road, connecting 13 times in 48 advantages (27.1 per cent) in 14 games, and the top penalty-killing unit away from home, turning aside 39 of 42 short-handed situations (92.9 per cent).
Danny Briere nearly got the Canadiens on the board 6:05 into the second, but he was snuffed on his jam attempts at the left post by Nabokov. The Islanders held a 7-6 shots advantage in the period, closing the overall gap to 17-6 through 40 minutes.
There was playful banter within the somewhat sparse crowd on a snowy night on Long Island.
Many fans in red Canadiens gear made themselves heard throughout the game with chants of "Let's Go Habs" that were quickly met with boos from the Islanders faithful.
NOTES: The Islanders held a pregame moment of silence in memory of those killed last year in a shooting rampage at Sandy Hook Elementary School in Connecticut. ... Canadiens enforcer George Parros didn't return after a punch from Eric Boulton knocked him to his knees during a first-period fight. Parros didn't dress in 13 of the previous 16 games. ... Tavares and Thomas Vanek had three-game point streaks snapped.