NEW YORK — It’s not often you see a player smile from ear to ear after being checked head over heels into the opposing bench.

Torrey Mitchell was in full stride, trying to make sure he gained the red line before dumping the puck into the New York Rangers zone. His Montreal Canadiens were clinging to a 3-1 lead with 1:20 remaining in the third period of Sunday’s Game 3, and he was going to do everything it took to make the right play — even if it meant taking the full brunt of Kevin Klein’s 206 pound-frame slamming into him.

Call it just one sacrifice made in a game that featured many by the Canadiens, who took a 2-1 lead in their first-round Stanley Cup Playoff series with the Rangers and wrestled back home-ice advantage with their win at Madison Square Garden.

“I thought our guys were really focused from start to finish,” said Canadiens coach Claude Julien.

It was plain to see.

Whether it was the way the Canadiens pressed in the offensive zone and notched 29 shots; or the way they blocked up the neutral zone and only allowed 21 pucks to get to their net; or the opportunism they showed in scoring on two of three power plays; or the determination they had on three penalty kills — not surrendering a shot, let alone a goal to remain perfect in the category for the series — they had it going on.

Julien was asked what he felt was the most satisfying aspect of his team’s win.

“You’re asking me a question that I don’t think I can answer because I thought we did a lot of things well,” he said. “To win 3-1 is one thing, but I thought we did great defensively keeping [the Rangers] down to 12 shots [through two periods]. We did give some opportunities there late in the game, but we also did a great job of managing the game as we went along there.

“We’re the road team, and I thought we had to play smart, and we did that throughout the whole game. So I just thought overall it was a solid game, so I don’t think I can pinpoint one area that was more dominant than the other. It was a solid 60 minutes.”

A confidence-builder, really.

The Canadiens had opened these playoffs with a 2-0 loss on home ice last Wednesday. They faced a lot of questions about their ability to score after averaging less than 2.5 goals per game over the final two months of their regular season, and they answered them in Game 2 with four goals and a 58-shot performance that gave them the wind in their sails to deliver their best in Game 3.

“We just played so much smarter,” said sparkplug forward Brendan Gallagher, who assisted on Artturi Lehkonen’s goal, which gave the Canadiens a 1-0 lead with only 2:23 remaining in the second period.

It was the 21-year-old’s rookie’s first-ever playoff goal, rifled into the top corner of Henrik Lundqvist’s net and celebrated with ferocity.

When Mats Zuccarello cross-checked Andrei Markov in the face at the 4:05 mark of the third period, drawing a double-minor for high-sticking, you could sense the game was going to come down to whether or not the Canadiens could add insurance.

They did when Alexander Radulov picked up his fourth point of the series by making a gorgeous pass to Alex Galchenyuk, who shifted his way to the middle of the slot and fed Shea Weber a gimme for his first playoff goal as a Canadien.

When Radulov iced the game just under eight minutes later, with a backhand-forehand-one-handed-backhand finish that silenced the crowd, you could see the air coming out of the Rangers’ balloon.

It was their sixth straight playoff loss in front of their fans dating back to 2015, and it certainly left a bitter taste in their mouths.

“Anytime you’re not having success, or getting chances, getting opportunities, there’s definitely some frustration,” said Rangers forward Rick Nash.

The Canadiens found their best game in this one and made it a trying experience for their counterparts.

“They’re playing very well defensively,” said Rangers coach Alain Vigneault. “You have to give them a lot of credit.”

Considering Rangers J.T. Miller, Chris Kreider, Kevin Hayes and Derek Stepan each scored more than 45 points this season and have combined for one in this series, it speaks to the job the Canadiens are doing.

Everyone in bleu, blanc et rouge is in on the act, too; from a guy who’s known for his defensive chops in Weber, who played 52 seconds shy of half the game, to an offensive guy like Radulov, who made a tremendous defensive play on Ryan McDonagh in the dying seconds of the second period and was diving to get pucks out of the Canadiens zone while the Rangers had an extra attacker on over the final four minutes of the game.

“To win in the playoffs, you can’t afford to have any weak links at any time,” said Julien.

To keep winning in the playoffs, you need to leave both the good and bad performances behind you.

“Claude just gave us a speech: ‘You can enjoy it, but you can’t be satisfied,’ said Gallagher.

When he said it he was smiling as wide as Mitchell did after taking that hit.