CLEVELAND — The deeper and tougher Knicks had little trouble overpowering and vanquishing the Cavaliers in the end, even with negligible contributions for most of the first round from their lone All-Star.

One game after Julius Randle had been benched for the entire fourth quarter of Sunday’s win at Madison Square Garden, he reinjured his left ankle late in the second quarter and didn’t play in the second half.

And Tom Thibodeau’s gritty squad absorbed every punch once more and prevailed yet again to advance to a second-round date with the Heat.

Jalen Brunson finished with a team-high 23 points and Obi Toppin filled in ably for Randle in the second half as the Knicks dispatched the Cavs in five games, finishing them off without their leading scorer for the final two quarters of a series-sealing 106-95 victory Wednesday night at a silenced Rocket Mortgage FieldHouse.

Thibodeau and the Knicks deservedly will make the franchise’s first trip to the second round of the playoffs since 2013 and only their second since 2000.

And they incredibly will have home-court advantage with the second round starting Sunday (1 p.m.) at the Garden after Jimmy Butler and No. 8 Miami shocked the top-seeded Bucks in overtime in Game 5 Wednesday night in Milwaukee.

“I think the way this team plays, it resonates with all our fans. They play hard, they play smart and they play together. And I think if you do that in New York, it’s always recognized,” Thibodeau said afterward. “But there’s still a lot of work to be done. We have a lot of areas to improve upon. So we’re looking forward to the next challenge.”

RJ Barrett capped a strong final three games of the series with 21 points on 7-for-13 shooting, and Josh Hart started in place of Quentin Grimes again and registered 12 rebounds in 47 heartbeat minutes, including the entire second half.

Sixth Man runner-up Immanuel Quickley also snapped out of his series-long scoring slump with 19 points off the bench, and Toppin netted all of his 12 in the third quarter with Randle sidelined, contributing two 3-pointers and a couple of rim-rattling dunks.

“We’ve had a ‘next man up’ mentality all year, so when a guy goes down, the next guy steps up, it’s a part of having such a great team, and we definitely want those guys to come back,” Barrett said. “So we’ll be waiting for that, seeing how that goes.

“But whoever’s on the floor for us is going to play their heart out and give everything they have. It’s called a team…. As a team, we have so many weapons.”

Mitchell Robinson also completed a dominant series against overmatched Cleveland bigs Jarrett Allen and Evan Mobley with 13 points and 18 rebounds, including an astonishing 11 more on the offensive glass, plus two deflating put-back dunks late in the fourth quarter

All-Star guard Donovan Mitchell scored 28 points for the Cavs, but the Westchester product’s season was ended by his hometown team after the Knicks were unable to obtain him from the Jazz last summer.

Randle had 13 points before departing just before the end of the second quarter after reinjuring the sprained left ankle that had kept him out of the final five games of the regular season.

Randle dished out five assists in the opening period and netted seven points as the Knicks carried a 33-26 advantage through one.

The All-Star power forward’s strong half came to an abrupt end when he landed on Caris LeVert’s foot with 1:17 left before halftime, and he hobbled into the locker room before returning to the bench in street clothes in the second half.

The Knicks still led 61-51 at intermission, with Brunson scoring 17 points, while Barrett and Quickley contributed 11 apiece on a combined 9-for-13 from the floor.

With Randle out, Toppin knocked down a corner 3 to open the third and then put the Knicks back up by 13 with a crowd-silencing windmill slam in the open court off a headman feed from Hart. He scored 12 points in the quarter as the Knicks led 87-75 heading into the final period.

A driving bucket and a pull-up jumper by Darius Garland closed the gap to six with eight minutes to play, but Barrett and Quickley sank two free throws apiece to restore the lead to double digits.

Hart’s lob pass found Robinson for another dunk and a 96-84 advantage with under five minutes remaining before the Knicks’ first postseason advancement in a decade was completed.

“I think it means a lot, something to be happy about in the short term,” Brunson said. “We get to play more basketball, and whenever we get to do that, it gives us another opportunity to get better and move forward and continue to see where we can go.”