Brock Boeser in regulation scored for Vancouver (10-15-2), who improved to 2-0 under newly minted head coach Bruce Boudreau.
Patrice Bergeron got a power-play goal for Boston (12-8-2) on a five-on-three advantage early in the third.
Canucks goalie Thatcher Demko registered 35 saves to collect a win on his 26th birthday. Jeremy Swayman stopped 31-of-32 shots.
It's the first time this season the Canucks have won two games in a row at home.
The Canucks took a 1-0 lead into the third period but were outshot 16-13 across the final frame.
Boston got a two-man advantage early in the third period and used the opportunity to knot the score at 1-1.
Juho Lammikko was called for slashing and the Canucks were weathering the penalty before Miller ran into Swayman and was called for goaltender interference.
Just seconds into the five-on-three stretch, David Pastrnak sent a shot flying from inside the blue line and Bergeron deflected it in from in front of the net 4:51 into the final frame.
It was the ninth goal of the season for the Bruins captain.
Bruins villain Brad Marchand flattened Travis Hamonic along the boards midway through the second frame, leaving the Canucks defenceman with an apparent leg injury. Hamonic limped to the bench, not putting any weight on his right leg, and was helped down the tunnel by a trainer. He did not return to the game.
Marchand was handed an interference penalty for the play and the Canucks capitalized at the 15:01 mark.
Miller uncorked a rocket from the top of the faceoff circle and Boeser tipped it in past Swayman from low in the slot for his sixth goal of the season.
Both sides were one for four with the man advantage Wednesday.
The Bruins briefly had reason to celebrate earlier in the second. Boston picked off a puck deep in Vancouver territory and got it up the wall to Erik Haula, who went one-on-one with Demko before sending a backhanded shot up over the goalie's left pad.
The revelry was brief, though, as the Canucks challenged for offside and after a video review, officials called the goal off.
Boston will be back in action Thursday, visiting the Oilers in Edmonton. Vancouver continues a six-game homestand Friday when it hosts the Winnipeg Jets.
NOTES: The Canucks lost 3-2 to the Bruins in Boston on Nov. 28. Canucks defenceman Oliver Ekman-Larsson was scratched from the lineup with an undisclosed injury. Miller has seven points (two goals, five assists) in his last five games.