MIAMI — The Knicks sit on the brink of elimination. And they deserve that position.

Outcoached, outhustled, outclassed and punked again, New York fell Monday night to the Miami Heat, 109-101, with Julius Randle disappearing in a pivotal moment and Jalen Brunson unable to carry the stragglers past Jimmy Butler.

Randle continued his series to forget by fouling out with about three minutes left. He went scoreless in the fourth quarter, taking just one shot in the final period as the Heat’s lead remained steady.

The Knicks, trailing 3-1 in the series, could be eliminated with a loss Wednesday at home.

“Just maybe they want it more, I don’t know,” Randle said. “That’s been who we are all year.”

Brunson tried his best in the final minutes and finished with 32 points and 11 assists, but the Knicks were dominated in too many areas. They gave up 13 offensive rebounds — including seven in the fourth quarter — and were generally bullied in the paint by Bam Adebayo.

The Heat, which got 27 points and 10 assists from Butler, led for the final three quarters. The game was less competitive than the final score. It never felt like the Knicks would find the heart to win.

Randle’s box score showed improvement from his Game 3 disaster. His 20 points on 13 shots appeared efficient. But the fourth-quarter disappearing act spoke the loudest. He and coach Tom Thibodeau passively lamented the officiating, complaining without crossing the line of drawing a fine.

“That was tough. As far as officiating, that was one of the toughest games I’ve been a part of,” Randle said. “Usually the physicality in the playoffs is up. I had six fouls and maybe four of them were offensive fouls or five. That’s never happened in my career. That’s tough.”

Despite the gripes, the Knicks took more foul shots than the Heat.

“They say marginal contact; they’re calling charges one way for them,” Thibodeau said. “Jalen is taking it square on the numbers, it’s not…. I don’t wanna put it on the officials. I’d rather look at the film first before I comment further on that.”

With the offense in a funk and an ugly Game 3 to ponder, Thibodeau altered his starting lineup by replacing Josh Hart with Quentin Grimes.

It was the natural attempt to unlock 3-point shooting. Grimes, who started for the most of the season, had been struggling mightily since heading to the bench at the start of this series. A big part of the reasoning behind starting Hart was matching him up with Butler.

So Grimes instead drew the Butler assignment in the first and third quarters, and it was a mixed bag. The offense picked up a little as Grimes hit three 3-pointers. But Butler still worked his magic and controlled his minutes. Grimes’ biggest play of the evening was his dunk attempt in the second quarter, when the Knicks guard went for the highlight slam and was rejected at the rim by Butler.

It was an amazing display of athleticism from Butler, who apparently felt fine after reaggravating his sprained ankle in Game 3. His block was in the middle of a 13-6 run that gave Miami an 11-point edge.

“I don’t know, I got lucky,” Butler said coyly of the rejection. “I normally don’t block shots like that. I go for strips. But I got a piece of the ball.”

The Knicks were missing their sixth man, Immanuel Quickley, who was ruled out because of the ankle sprain suffered two days earlier in Game 3. He was labeled doubtful on Sunday and arrived for Monday’s game in a walking boot, ending hopes of a surprise appearance from New York’s sixth man.

Quickley’s status for Wednesday’s game is up in the air.

As a result of his absence, Brunson took on greater loads with 44 minutes. Miles McBride, the second-year defensive specialist, got a small role in the rotation. He went scoreless.

Mitchell Robinson was again outdueled by Adebayo, who finished with 23 points and 13 rebounds. Robinson, a top flight rebounder during the regular season and in the first round against Cleveland, only managed seven boards in his 33 minutes of struggle.

“Hell yeah I’m disappointed, that’s what I do [rebounding]. And I’ve been stopped from doing it,” Robinson said.