MONTREAL — Players on the Rangers’ bench said they had never seen Mats Zuccarello and Derek Stepan jump so high.

“You’re in the zone and you see that one go in, you just kind of lose it a little bit. It was a big goal for us,” said Zuccarello, still grinning more than 20 minutes after Mika Zibanejad’s goal gave the Rangers a thrilling 3-2 overtime win over the Canadiens on Thursday night in Game 5 of their playoff series. “Every game is like the biggest one of the season.”

After Chris Kreider’s shot bounced off a Canadiens defenseman’s skate, Zibanejad scooped up the loose puck and beat Carey Price at 14:22 of overtime to give the Rangers a 3-2 lead in the best-of-seven series.

“It’s a good feeling,’’ Zibanejad said. “I told myself I was going to go to the net [on the winner], and I was able to be in the right spot. Lucky. I saw it went in and after that, I blacked out.”

The Blueshirts can eliminate the Canadiens with a win in Game 6 on Saturday night at the Garden. If they do advance to the second round, they’ll face Ottawa or Boston. The Senators lead the Bruins three games to one in their first-round series.

Zibanejad had only one assist in the first four games of the series. “I felt I didn’t do enough to make plays, and that’s the type of player I need to be,” he said.

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The goal was Zibanejad’s biggest since he arrived from Ottawa in the Derick Brassard trade last summer. He also had sent a pretty pass to Jesper Fast for a shorthanded goal that tied the score at 1.

It was the second overtime game in this exceedingly tight series; the Canadiens won Game 2 here on Alexander Radulov’s goal after tying the score with 17.3 seconds left in the third period. But Thursday night marked the second road win for the Blueshirts at Bell Centre.

Unlike the overtime loss last week, the Rangers found another gear and outshot the Canadiens 10-3 in the extra session. “We had some really good shifts and just came in waves,” Dan Girardi said. “We just kept coming and coming . . . We knew it was only a matter of time until we broke through.”

Kreider, who swung and missed on a beautiful setup pass to the left of Price earlier in overtime, said “part of the reason I whiffed was that I saw him coming across. When Mika scored, I was pretty happy. There was stuff we didn’t do a few nights ago in overtime; we harped on it as a group. Just try to make plays and continue to press.”

From the outset, it was clear that these were not the same Canadiens who lost in New York in Game 4. Their effort was admirable, if chippy, as hitting and swinging sticks flourished after the whistle, often without penalty. Again, Henrik Lundqvist (34 saves) had to keep the Rangers in the game.

In the four previous games, the team that scored first won. Artturi Lehkonen’s wraparound at the right post after Marc Staal’s turnover gave the Canadiens a 1-0 lead at 12:07. But the Rangers rallied from 1-0 and 2-1 deficits on goals from Fast and Brady Skjei, and there were close calls in the third.

With the Rangers trailing 2-1 in the second, Ryan McDonagh slashed Dwight King at 1:26 and Zuccarello went off for a high-stick at 3:30. They dodged those bullets. “When we needed the kills, we got them,” Girardi said.

With Rick Nash and Jimmy Vesey causing chaos in front, Skjei’s wrister beat Price from 12 feet with 1:32 left in the second to pull the Rangers into a 2-2 tie. That was a momentum-changer.

An earlier momentum swing came with the score tied at 1. Just 24 seconds after Fast’s goal, Brendan Gallagher beat Lundqvist over his glove on the power play to restore the lead. It could have been a crusher.

But after the pivotal win, Girardi said, “Now we’re hoping we can bring a good amount of momentum back to New York.”

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