Brendan Gallagher also scored for Montreal (18-10-2), while Max Pacioretty added an empty-net goal at 19:59 of the third. Carey Price stopped 15 shots.
Derek Dorsett was the lone goal scorer for Vancouver (18-9-2). Ryan Miller made 21 saves in defeat.
The game marked the end of a seven-game road trip that had the Canucks go 3-3-1.
Meanwhile the Canadiens, which ended a three-game skid, are now 15-1-1 when tied or leading after two periods.
Plekanec scored the game-winner at 15:44 of the final frame after tipping a beautiful pass from youngster Sven Andrighetto into the roof of the net.
Prior to puck drop, the Canadiens honoured the late Jean Beliveau with a video tribute, moment of silence, and lengthy standing ovation. The Canadiens great passed away last Tuesday at the age of 83. Beliveau's wife, his daughter and his granddaughters were in attendance.
Shortly after the end of the ceremony, Nick Bonino came a hair from putting the Canucks ahead just one minute into the contest, but Price made a diving save to his right to keep the puck out.
After going scoreless in the first period for the 22nd time this season, Montreal came out firing in the second. Benefiting from a two-man advantage for more than a minute to begin the middle frame, the Habs came close to breaking the deadlock on a few occasions.
Michel Therrien's men finally got their breakthrough when Gallagher's seemingly harmless shot from the face-off circle beat Miller glove-side into the top corner of the net at 6:56. The goal was Gallagher's third since signing a six-year contract extension with Montreal on Nov. 29.
The Canucks wasted little time finding their equalizer, with Dorsett beating Price exactly five minutes after the Canadiens opened the scoring. Dorsett scored Vancouver's fourth shorthanded goal of the season after taking a cross-ice feed from Jannik Hansen on an odd-man rush with Brad Richardson in the box.
Vancouver blocked 20 shots through two periods.
This was the second and final meeting between Montreal and Vancouver this season.
Notes: Lars Eller missed the encounter with an upper-body injury. Mike Weaver, who suffered a concussion against the Stars on Saturday, was also out of the lineup. ... Nathan Beaulieu, recalled from Hamilton on Monday, dressed for Montreal for the first time in three weeks. … The Canadiens have scored a league-low nine first-period goals this year. … The Canucks have not scored a power-play goal in their last four games (0-for-13).