Tuukka Rask stopped 27-of-28 shots for Boston, which logged a second straight victory and sixth in seven games.
Daniel Paille also scored.
Defenseman Raphael Diaz got the only goal for the reeling Canucks, who dropped a fifth consecutive game.
Roberto Luongo turned aside 29-of-32 shots.
2014: The Year in Fashion [PHOTOS]
LeBron James reveals his new Nike shoes