"It's fun, obviously," Bozak said. "It's exciting when you win in overtime. Last year kind of helped us in moments like that to not panic and just stick with it and try and play our game and that's what we've done and luckily been on the winning end of them.
"To hold those guys to one is pretty good (Vancouver scored at least five goals in five of its previous six games). They got a lot of firepower. That starts with [Binnington], and our D always does a good job of limiting chances."
Markstrom made 25 saves, and Quinn Hughes scored late in the third period for the Canucks (9-3-3), who extended their point streak to eight games (5-0-3).
"That was a big-boy game," Vancouver coach Travis Green said. "That's a heavy team. They know how to win. If you want to win a Stanley Cup, you've got to play in some heavy games. That game was probably the most physical game we've been in this season. Our team handled it very well."
Bozak put the Blues ahead 1-0 at 3:37 of the second period with his first goal of the season. Following a turnover along the boards by Canucks defenseman Jordie Benn, Bozak skated to the slot and took a pass from Sammy Blais before beating Markstrom with a wrist shot over the goalie's shoulder.
"We had a lot of offensive-zone time, just cycling, and I was able to get open in the slot and [Alexander] Steen and Sammy made a great play to get me the puck," Bozak said. "It was nice to finally get one this year, a little relief."
Hughes, who returned to the lineup after missing one game because of a bruised knee, tied the game 1-1 at 16:25 of the third with a shot from the left point that made it through a screen by Elias Pettersson.
"We're a motivated group. We wanted two points," Hughes said. "We pushed them pretty hard. They are a really good team. For us, it's encouraging. We just need to keep going."
Binnington stopped Pettersson on a breakaway at 2:17 of the first period, Miller alone in front of the net at 11:35 of the first, and got his pad down to deny Brandon Sutter on a shorthanded breakaway at 10:45 of the third.
"We're used to that now every game we play," Bozak said. "It's almost funny, we kind of expect that from him just because we've seen it so much, but he just keeps on amazing us every single game, holding down the fort and giving us a chance to win."