Andrei Markov added his 100th career goal for the Canadiens, who posted their eighth win in nine games.
Tuukka Rask stopped 22 shots, but feel to 3-12-3 in his career during the regular season against the Canadiens.
Montreal improved to 3-0 against Boston this season.
It was the 728th regular season meeting between the clubs, the first in Boston since Montreal upset the top-seeded Bruins in a seven-game series last spring in the Eastern Conference playoff's second round.
The Canadiens beat the Bruins 5-1 on Nov. 13. Since that loss, the Bruins had won three straight, allowing only four total goals.
Montreal went up on Markov's goal 11:37 into the first period.
Skating on a power play, Plekanec won a faceoff to Brendan Gallagher, who slipped a short pass to Markov. He fired a wrist shot that beat Rask on the stick side inside the post, giving the Canadiens their first road power-play goal this season after going 0 or 29.
Boston controlled play after the goal, outshooting Montreal 8-1, but the chances were relatively weak.
Montreal then made it 2-0 on Plekanec's goal midway into the second when he scored at the end of a 3-on-2 break after the Bruins failed to get a shot off during an odd-man rush.
There were plenty of hard checks between the longtime rivals, the best coming when Bruins winger Daniel Paille sent Alexei Emelin into his own bench early in the second.
Chats of "Go Habs Go!" could be heard a few times from a fairly large gathering of red-jersey wearing Canadiens' fans spread throughout TD Garden, but they were quickly silenced by "Let's Go Bruins!"