The Rangers were 20 minutes away from advancing to the Eastern Conference Final at Madison Square Garden on Monday night, and the Hurricanes knew it.
“You go into the third period and realize it could be the last period of the season,’’ Carolina’s Evgeny Kuznetsov said.
Instead, the Hurricanes — held scoreless for the first two periods — scored four times in the third to beat the Rangers, 4-1, to force a Game 6 in Carolina. 
“It’s a dogfight right now,’’ said Kuznetsov, who scored the game-winner at 6:39 of the third.
Jordan Staal had tied the game 1-1 at 3:33 of the third and the Rangers never recovered.
Now, the Canes have as much life as they’ve had in this series, but they know they are still just one loss away from elimination.
“They bought us another day,’’ head coach Rod Brind’Amour said.
Heading into the game, the Hurricanes acknowledged their precarious position, trying to overcome a 3-0 deficit in the series before winning Game 4 in Carolina to bring the series back to the Garden.
And now, they head down to Raleigh, N.C., again for Game 6, with the pressure creeping in on the Rangers.
“We were down 3-0 [in the series] so quick, it was like we didn’t even know what happened,” Carolina’s Martin Necas said. “Then we started playing our game. We’ve got [playoff] experience in this room, which is big.”
And they have something else now.
“We believe in this locker room,’’ Necas said. “We’re not satisfied. We’re going back home.”
The tone of the game — and perhaps the series — changed with Staal’s goal, a nifty backhand that got by Shesterkin.
“We trusted our game, and we live to play another day,’’ Staal said. “We knew we had to play our best period and we did. We’re fighting for our lives.”
That won’t change in Game 6.
“It’s not gonna be easy,’’ Dmitry Orlov said. “It gets harder now.”
“There’s a lot of pressure on both sides when you’re fighting for your lives,’’ Staal said. “We were clawing with fingernails.”
The intensity figures to increase for Game 6, with the Hurricanes now with a much more realistic chance of forcing Game 7 and pulling off a historic comeback.
“We had a high level of desperation,’’ Brind’Amour said of Game 5. “There had to be.”
But the team’s confidence, the coach said, “that’s been there all along.”
