The Bruins appeared to have the Vancouver Canucks gripped by the collar with their collective fist cocked for the knockout punch all night on Saturday at the Garden. But the suddenly tenacious Canucks bobbed, weaved and came away with a 5-4 shootoout win in a highly entertaining game.

After the B’s coughed up a one-goal third period lead, Andrew Peeke tied the game late in the third to get it to extra sessions. The B’s, who outshot Vancouver 42-22 in regulation and OT, had numerous chances to win it in overtime but could not get the handle on numerous glittering chances before losing in the skills competition.

The B’s were at least partially undone by an uncharacteristic looseness before that.

“I think it was just some individual mistakes, for some reason,” said coach Marco Sturm. “We had a really good first period. We should have put them away, or have a little bigger cushion…It’s unfortunate, because I thought we were ready to go today in the first period and couldn’t find a way to put them away.”

The shootout went seven rounds and Liam Ohgren was the only player to score, beating Jeremy Swayman with a backhander. In an unusual move, Marco Sturm gave Peeke a chance to win it in the fourth round but  he was denied. And after Ohgren scored what turned out to be the winner, Kevin Lankinen stoned Morgan Geekie to nail down the win.

The eyebrow-raising choice of the stay-at-home defenseman Peeke was more than a gut instinct, said Sturm.

“We practice it all the time and he did one move and he did it real well, not just once but a few times,” said Sturm. “I thought he was going to do it again and he didn’t. That’s why I picked him. So that’s on me. That’s all.”

Peeke went with a forehand wrister that Lankinen was able to stop. Had Peeke scored at that juncture, it would have won the game and brought the house down. But it didn’t,  and Ohgren was the hero for Vancouver.

It was the first extra session loss of the year for the B’s and it was a point that got away, to be sure. They had also gone into the game 16-0-0 when taking a lead into the third period, a mark that now stands at 16-0-1.

“We know we have to play a full 60 minutes to win games in this league,” said Tanner Jeannot. “Tonight, going into the third period with a goal lead, it was just too loose and we’ve got to clean that up.”

The Bruins dominated the first period, outshooting the Canucks 13-4, but they only managed to go into the first intermission even with their guests.

The B’s went into the game unhappy with how they attacked the explosive but defensively suspect Oilers in Thursday’s 3-1 loss. And while the Canucks had come into the game having won three straight and playing their best hockey of the season after trading superstar Quinn Hughes, the focus in the B’s room was on themselves and not their opponent.

And it was a pretty big game for the B’s to boot. After losing the previous two of three games, they were on the outside looking in to the playoff bracket to start the day and Atlantic Division foes Detroit and Ottawa had already won their matinees. The B’s couldn’t afford to slip any further down the ladder.

The B’s appeared ready to meet the moment. They were all over the Canucks to start the game, earning two power plays and scoring on the first one.

Geekie scored his 25th of the season at 8:23 and wired a one-timer past goalie Kevin Lankinen to what felt would be a solid performance.

But with 13.9 seconds left in the period, the Canucks got on the board. Linus Karlsson caved in Hampus Lindholm low along the boards and got it to Ohgren, one of the players who came back in the Hughes trade, below the goal line. Ohgren dished it out front to Max Sasson, who snapped a quick wrister that beat Jeremy Swayman shortside.

All of a sudden, what was an excellent opening 20 minutes turned into nothing more than a push for the B’s.

That late goal changed the tenor of the game and, at 4:22 of the second, Vancouver had its first lead when the B’s gave up their seventh power-play goal in six games. With Mikey Eyssimont in the box for high sticking, the Canucks made it 2-1 on a gaffe from Swayman. Filip Hronek rimmed the puck along the dasher and Swayman came out behind his net to make a routine play on it. But the puck had some mustard on it and Swayman couldn’t stop it. It went to Evander Kane in the corner and, with Swayman still scrambling to get back in the net, Kane fed Karlsson out front for an easy goal.

“It popped right over my stick,” said Swayman, shaking his head. “You want to get back and compete, but just an unfortunate bounce.”

With the B’s playing back-to-backs this weekend — Atlantic Division foe Ottawa is here on Sunday night — it was a mild surprise that Swayman got the call, as it was his fourth consecutive start.

“It was a big game and we thought he would give us the best chance,” said Sturm.

But the B’s regained the lead before the period was out.

They tied it up on a 4-on-4 at 9:41 with Jeffrey Viel and Kane in the box for roughing. After Swayman stoned old friend Jake DeBrusk on a clean breakaway, the B’s evened it up on a pretty play that Pavel Zacha started and finished. Zacha came out of a D-zone scrum with the puck and sent it out to Casey Mittelstadt to begin the rush. Once he gained the zone, Mittelstadt fed the rushing Nikita Zadorov, who took the puck down the middle then wide before passing it back for a Zacha tap-in, his 10th of the year.

The B’s then regained the lead at 12:05 on another beauty. After the B’s had gained the zone on an odd-man rush, the reunited third line cashed in after a nice keep-in from Victor Soderstrom. Fraser Minten fed the puck down low to Mark Kastelic, who made a superb backhand pass through the slot to Jeannot for Jeannot’s fourth.

It appeared that the Canucks had tied it up again at 17:16 when Hronek’s blue line shot bounced around the slot and landed in the net behind Swayman. But upon review, it was clear that the last bounce went off defenseman Marcus Petterson’s glove and the goal came off the board.

The B’s held a 28-12 shot advantage through two periods but just a one-goal lead.

They could not hold it. After the B’s could not cash in on a early third period power play, the Canucks tied it again when Karlsson pounced on a loose puck near the Boston blue line and beat Swayman with a bar-down wrister at 3:53 of the third.

Then the Canucks regained the lead at 7:34. After a couple of Bruin icings and a lost faceoff, Ohgren tipped home a Petterson blue line shot to make it 4-3 and the B’s were in jeopardy.

The B’s then really started taking aim at their feet. With 19 seconds left on a Charlie McAvoy slashing penalty, Hampus Lindholm took a tripping penalty.

They managed to kill off both of them but that took a chunk of time off the clock.

Still, with 3:44 remaining in the third, Peeke evened it up with his third of the season when his seeing-eye snap shot hit the post, bounced off of Lankinen and in.

That, however, was the last puck to beat the Vancouver backup.