Henrik Sedin replied for Vancouver (3-3-0), which got 34 saves from Roberto Luongo in a matchup of potential starting goalies for Canada at the 2014 Winter Games. Luongo also stopped Pacioretty on a third-period penalty shot.
The winner came in the second period with the Canadiens killing a penalty. Canucks defencemen Dan Hamhuis and Jason Garrison got tangled up behind the Vancouver net on a breakout, with the puck caroming into the crease and off both of Luongo's skates before dribbling over the line at 16:12.
Eller, who wasn't even in the Canucks zone at the time of the goal, was the last Canadiens player to touch the puck for a Montreal team that didn't score a short-handed at all last season or through the first four games of 2013-2014.
Apart from that bizarre play, the story for a lot of the game was the play of Price and Luongo, with the pair matching each other save for save at times.
Down 2-1 after the Eller goal late in the second period, Luongo held the Canucks in it early in the third, including a stick save on Pacioretty's penalty shot attempt after the Canadiens forward was hooked down by Vancouver defenceman Kevin Bieksa.
But the Canadiens extended their lead at 6:46 on the power play. P.K. Subban just held the puck in at the line and it eventually found its way to fellow Montreal defenceman Andrei Markov down low, who fed a wide open Plekanec for a tap-in past a helpless Luongo.
Canucks head coach John Tortorella has been preaching a shoot-from-anywhere mentality, but his team failed to test Price until Bieska's effort from outside the Montreal blue-line with nearly 11 minutes gone in the period.
Gorges then made it 4-1 with a shot through traffic that Luongo didn't see, much to the delight of the large contingent of Canadiens fans in attendance at Rogers Arena.
The final buzzer sounded with those same supporters serenading their team with the well-known "Ole, Ole, Ole" song.
The Canucks kept up the pressure and were rewarded a bit later on when the Canadiens couldn't get the puck out of their zone. Daniel Sedin picked up a rebound from Garrison at the side of the net and fed a blind behind-the-back pass to Henrik Sedin, who scored his first of the season — and 799th point of his career — at 13:12 to tie the score.
But it all went south for Canucks, who start a season-long seven-game road trip on Tuesday in Philadelphia against the Flyers, exactly three minutes later with Eller's winner.
Pacioretty drew a hooking penalty on Canucks defenceman Chris Tanev early in the first period before making Vancouver pay with his second goal of the season. The Habs forward took a pass in the slot with Montreal on the man advantage and fired a shot through Luongo's pads that just dribbled across the line.
The goal was the first surrendered by the Canucks' penalty killing unit this season after starting a perfect 18 for 18 through five games.
Price was the story for much of the rest of the opening 20 minutes, with a big rebound stop on Garrison on a Canucks' power play midway through the period. He then made a desperation save on Daniel Sedin with five minutes to go, which brought chants of "Carey, Carey" from Canadiens fans.
Notes: The Canadiens were without captain Brain Gionta because of what the team called "family reasons." ... Canucks defenceman Alexander Edler served the first game of a three-game suspension for his hit to the head of San Jose Sharks forward Tomas Hertl on Thursday night. ... Canucks forward Zack Kassian returned to the lineup after serving his eight-game suspension for breaking the jaw of Edmonton Oilers forward Sam Gagner with a high stick in the pre-season. ... Vancouver's seven-game road trip also includes games against the Buffalo Sabres, Pittsburgh Penguins, Columbus Blue Jackets, New York Islanders, New Jersey Devils and St. Louis Blues. The Canucks' next home game is Oct. 28 against the Washington Capitals. ... Montreal's next game is Tuesday in Winnipeg against the Jets before returning to the Bell Centre for a five-game homestand.