The Canucks winger patiently outwaited Bruins goalie Jeremy Swayman, and tucked a shot in behind his right skate. Bo Horvat also scored in the shootout.
Brock Boeser scored in regulation for Vancouver, which improved to 2-0 under new coach Bruce Boudreau.
''I think everyone feels confident that we can go into the next one and get another (win),'' said defenseman Quinn Hughes. ''We're taking it one game at a time and one week at a time and that was the message when coach came in. For the first two games, I think we're doing really good. And the amazing thing is I think we can play better, too.''
Boudreau took over the team late Sunday night and has had little time to come up with a shootout strategy. He said he relied on statistics Wednesday.
''I wanted (Elias Pettersson) to go first. I think he was at 40% in his career,'' the coach said of the Swedish center who was stymied by Swayman. ''And then J.T. I know loves the pressure. I know that already after about four days.''
Patrice Bergeron got a power-play goal for Boston on a 5-on-3 advantage early in the third.
Canucks goalie Thatcher Demko made 35 saves on his 26th birthday. Swayman stopped 31 of 32 shots for Boston.
The Canucks won consecutive home games for the first time this season.
The Canucks took a 1-0 lead into the third period despite being outshot 16-13.
Boston got a two-man advantage early in the third period and tied the score at 1-all.
Juho Lammikko was called for slashing and the Canucks were working off the penalty before Miller ran into Swayman and was called for goaltender interference.
Just seconds into the 5-on-3 stretch, David Pastrnak sent a shot from inside the blue line and Bergeron deflected it in from in front of the net 4:51 into the third. It was the ninth goal of the season for the Bruins captain.
''Obviously (Pastrnak) has that shot where they need to be in the shooting lane, so it usually opens up a bit of a passing lane for a shot tip and especially 5-on-3 and we tried to use that to our advantage,'' the Bruins captain said. ''We talked about it before the face off on that play that it should be there.''
Brad Marchand flattened Vancouver's Travis Hamonic along the boards midway through the second frame, leaving the Canucks defenseman 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, leaving Vancouver with five defensemen.
''I think as far as the five going there, I think we played really good and strong,'' Hughes said. ''And it was just about playing smart hockey with five guys there and taking short shifts and I think we did really good with that.''
Marchand got an interference penalty for the play and the Canucks capitalized at the 15:01 mark.
Miller uncorked a shot 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 1 for 4 with the man advantage.
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 1-on-1 with Demko before sending a backhanded shot up over the goalie's left pad. The Canucks challenged for offside and after a video review, officials called the goal off.
Bruins assistant coach Joe Sacco said the game was tight at even strength.
''Both teams had some opportunities but probably not as much as we would have liked, especially speaking for our group. We had some opportunities,'' said Sacco, who's filling in as head coach while Bruce Cassidy is in COVID-19 protocol. ''We passed up on some shots, I thought. I'd like to see us play off the shot a little bit more at times, but some of that has to go their credit as well. They defended hard.''
NOTES: The Canucks lost 3-2 to the Bruins in Boston on Nov. 28. . Canucks defenseman 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.
Bruins: At Edmonton Oilers on Thursday for the second of a three-game trip.
Canucks: Host Winnipeg Jets on Friday in the fourth game of a six-game homestand.
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