Boeser made it 2-1 at 12:49 of the third period, shooting a bouncing puck past Swayman from the left face-off dot after a cross-ice pass from Nikita Zadorov.
The play started with Miller winning an offensive zone face-off.
"Whether we won or lost, I thought that we just played an awesome 60 minutes,” Miller said. “Sometimes they're going to go in and sometimes they're not.”
Boqvist put Boston ahead 1-0 at 5:27 of the second period on a breakaway from the hash marks after getting behind Hronek following a neutral zone face-off battle. Boqvist took a nice pass from Justin Brazeau, who was playing his third NHL game, around defenseman Quinn Hughes and scored on a forehand deke in tight around the outstretched right pad of Demko.
“I just found the puck and I heard the bench yell ‘two,’ so I tried to look over and put it to an area because I know how fast he is and how skilled he is,” Brazeau said. “So it was a nice play by him.”
Heinen made it 2-0 at 11:15, shoveling the puck inside the left post from the top of the crease after Trent Frederic’s wraparound attempt from the other side.
“I kind of know he's going to try to put it far post across the crease there, so just try to stay kind of backdoor and luckily I chipped it in,” Heinen said. “I guess that's where you got to go to score goals.”
Boston was outshot 17-5 in the third period and forced to play overtime for a fifth straight game.
“I just don't think we played the right hockey in the third period,” said defenseman Brandon Carlo. “From getting pucks north out of the [defensive] zone, to getting pucks behind them, playing the right style of game to kind of limit their chances, I don't think we did a good enough job at that.”
NOTES: Boeser has 33 goals this season, extending his NHL career high, but entered Saturday with just one in 10 games since playing in the NHL All-Star Game on Feb. 3. … Boston defenseman Matt Grzelcyk played 19:39 in his return after missing one game with a lower-body injury sustained early in a 6-5 overtime win against the Edmonton Oilers on Wednesday. … The Canucks matched their team record for wins through 60 games, a feat previously reached in 2011-12 and 2010-11, and they won the Presidents’ Trophy as the NHL’s top regular season team in each of those seasons.