CLEVELAND — The locals smelled blood. They had waited all afternoon, 19,432 of them, to set themselves loose on the Knicks and now they had them. A 92-84 Knicks lead with under four minutes to go had disappeared like a magic trick. The Cavaliers were up by a point now, 93-92, and the Knicks were about to turn in another empty possession at the worst possible time.

Except a funny thing happened on the way to the void.

Josh Hart had another idea.

“Got to be aggressive there,” Hart said.

Hart had the ball in his hand as the shot clock was speeding toward zero. He was 27 feet from the basket. Hart isn’t any of the first three Knicks you necessarily want to be shooting from 3-point range. Except that when the task at hand is the simplest one in the sport — win the damned game — he is exactly who you want with the ball in his hands.

“He plays to win,” Knicks coach Tom Thibodeau said. “There’s no other agenda other than winning.”

Said Jalen Brunson: “It’s unreal. It’s just what he does.”

Hart took the shot. Hart made the shot. There were still 109 seconds left in the game and after his shot, every one of them belonged to the Knicks. Brunson made a couple of shots. Both Isaiah Hartenstein and Julius Randle snared enormous offensive rebounds. Quentin Grimes knocked down a couple of ice-water free throws.

And the Knicks had themselves a 101-97 victory. The final buzzer kicked a plug out of the wall, silenced the locals and provided the Knicks their most important postseason win in — what, 10 years? Twenty-three years? Longer?

“We needed everyone,” Thibodeau said.

And everyone responded. Start with Randle, who opted to play after spending 17 days recovering from an ankle sprain, who knocked down his first shot, a 3, Willis-style. He scored 16 in the first half, and provided a spark of inspiration that his teammates took and ran with.

“I was tired as hell, for sure,” said Randle, who finished with 19 points, 10 rebounds and four assists. “But that’s why we have such a great team, able to lean on the guys, everybody able to pick each other up. I just go out and be myself and let the cards fall where they may and trust in the guys.”

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Brunson shook off early foul trouble and in the second half made a series of huge shots on the way to 27 points. Hartenstein was a plus-19 across 22 minutes. Hart was exactly what he has been since the Knicks acquired him at the trade deadline — smart, savvy, leading with his chin, and first in line to make a big play when a big play needs to be made.

“When you’re in adverse situations you either crumble or you band together and come out on top,” Hart said. “We didn’t get frustrated or rattled.”

It was an especially encouraging team-wide performance given how little collective playoff experience they have — starting with Hart, who was playing the first playoff game of his six-year pro career. Compound that with how, in the space of two minutes, the afternoon went from a blissful high to a dispiriting low and back to a gleeful high …

“That’s playoff basketball,” Thibodeau said.

Better, it’s winning playoff basketball. The Knicks had spoken all week about how they were not merely content to just get in the tournament. That’s what happened two years ago, and the resulting five-game ouster at the hands of the Hawks left a far more sour taste than a 41-31 season should have.

This time, it was the Cavs with Game 1 at home, and it was the Cavs who played nervously and shakily early, missing layups and foul shots. Donovan Mitchell didn’t miss much of anything, finishing with 38 points and eight assists. He dragged the Cavs back late, and it seemed like Mitchell would be all anyone would want to talk about when it was over.

Instead, by the end, as the Knicks rose one by one to make enormous play after enormous play, Mitchell was reduced to waving his arms, trying to exhort the crowd to distract Grimes as he stepped to the free-throw line with 4.1 seconds left and the Knicks up two. Even that didn’t work. Grimes coolly put the game away.

“Our game plan today was: just win,” Brunson said. “Whatever it took. Whatever was needed.”

It took a little elbow grease from everyone, and so the Knicks have seized home-court advantage, and get two days to rest for a house-money special Tuesday back here. Hart called all of it “fun.” And why would anyone argue?