After winning just once in their first eight games during their worst start to a season in 70 years, the Canadiens have put together two victories in as many nights.
Carey Price stopped 27 shots and allowed only a first-period, power-play goal to Patrice Bergeron.
Erik Cole tied it in the second period by tipping in a shot and Plekanec scored the go-ahead goal with 9:14 to play in the third.
The Bruins, coming off their first Stanley Cup title in 39 seasons, have opened the campaign with six losses in nine games.
Tim Thomas allowed both Montreal goals on 35 shots. The Canadiens broke out of their season-opening slump Wednesday with a 5-1 victory over Philadelphia.