The Knicks needed this one — what with a six-game Western swing looming ahead.

And Knicks coach Tom Thibodeau knew it. He was a raging inferno on the sidelines during a rollercoaster first half. He picked up a technical foul screaming at the referees and let loose on RJ Barrett on the bench after he had allowed two straight backdoor cuts to the Bulls — the last one by Lauri Markkanen.

Despite a topsy-turvy night, during which the Knicks took sizeable leads and the Bulls scrapped back multiple times, Thibodeau’s crew posted a 113-94 victory at the Garden on Wednesday, laying down the hammer with a spectacular 37-18 fourth quarter.

The Hawks lost at Philadelphia, so the Knicks regained sole possession of fourth place in the Eastern Conference — which would mean home-court advantage in the first round of the playoffs. The Knicks have won 10 of 11, and their magic number to clinch at least a play-in tournament berth fell to one.

Responding after they both had dud games Monday in rough loss to the Suns, Julius Randle and RJ Barrett were dynamos, combining for 56 points. Randle scored 34 points, while Barrett shook off the Thibodeau tongue-lashing to finish with 22 points, seven rebounds, six assists and two steals.

“It’s really his job to hold us accountable,’’ Barrett said. “I don’t take it personally. I was mad at myself, too. I knew before he said anything.’’

The 1-2 punch of Randle and Barrett combined to shoot 21-for-38 after combining for just 34 points in the Suns downer, which ended the Knicks’ nine-game winning streak.

“Phoenix is terrific team, but with a minute to go, we have a chance to win the game,’’ Thibodeau said. “We were upset we didn’t play our best, but what Julius has done all year and what RJ is doing — both of those guys are terrific. They’re not going to be great every game. Nobody in this league is.’’

Thibodeau thought nothing of his rant at Barrett.

“I see my job is to tell them the truth as I see it,’’ Thibodeau said. “Players in this league are great. They can beat you on a great play, but it shouldn’t happen over and over again. At our best, that doesn’t happen.’’

“We can easily handle it — we’re not a fragile group,’’ Randle said.

In the six-game homestand that started on April 18, the Knicks (35-28) went 5-1 — the first time they have posted a record that good on a six-game homestand since 2000.

“I think we can get better,’’ Randle said. “It’s just the details we miss at certain times. I’m excited for what this team can be and how much we can improve.’’

Thibodeau has been upset with the recent defensive play, and his club responded. Knicks defensive center Nerlens Noel recorded five blocks, including one late on Bulls stud center Nikola Vucevic (24 points), and added three steals. Noel also nearly sank a 3-pointer, but the ball went in and out.

“That was crazy,’’ rookie Immanuel Quickley said. “He almost hit a 3. I would’ve ran off the bench and tackled him.”

The Bulls, playing without star Zach LaVine (COVID-19 protocols), are still fighting for a top 10 play-in berth. They kept fighting and trailed by just 76-75 after three quarters.

Quickley and fellow rookie Obi Toppin started their wonderful final period. Quickley pumped in a 3-pointer and a jumper and scored 11 of his 13 points in the final frame.

After Quickley’s early barrage, Derrick Rose found Toppin for a beautiful alley-oop dunk. Toppin, the 2020 lottery pick who is playing with more verve, tipped in his own miss midway through the fourth to give the Knicks a 93-84 lead.

And now the Knicks are on a roll as they head to Houston to start the trip Sunday.

“Anytime we win, we’re going to be happy about it,’’ Randle said. “We go to the … road trip and looking forward to the challenge.’’