DETROIT — All game long, the crowd at Little Caesars Arena had directed its venom at one target, Jalen Brunson. And for 47 minutes and 56 seconds, he never looked at them, never acknowledged the chants and the curses.

And as he ran down the clock on the game, the series and Detroit’s dwindling season, he faked Ausar Thompson, sending him sliding away, and hit an open three-pointer with 4.3 seconds left to give the Knicks a 116-113 win over the Pistons in the sixth and final game of their first-round series.

This time Brunson, who finished with 40 points, stood at center court and blew a kiss to the crowd as the Pistons convened to strategize for one last chance, but a pass went off the fingers of Malik Beasley. When the Knicks inbounded the ball, OG Anunoby tossed it in the air and the Knicks finally could exhale and celebrate.

The Knicks now will turn to a matchup that has been on their minds since the summer rebuild, as they’ll face the Celtics in the Eastern Conference semifinals beginning Monday in Boston.

After taking a 15-point second-quarter lead, falling behind by halftime, taking a 12-point lead early in the fourth quarter and falling behind by seven, the Knicks closed the game with an 11-1 run.

“I think this game just shows a little bit of how our season has gone,” Karl-Anthony Towns said. “We’ve kind of made it difficult on ourselves and we’ve always taken the toughest path to getting the job done, and I think this series is just another way of showing how our season has gone and has prepared us for these moments where people question our grittiness, they question our belief in ourselves and how disciplined we can be, and I hope that this series answers a lot of questions about who this team is and the identity that New York basketball has always had.”

The identity undoubtedly is set by Brunson, but the Knicks showed a resilience on this night and really in the series, fighting to win three games in the din of the road arena (the visiting team won five of the six games in the series). The final four games were decided by a total of nine points.

The Knicks scored only nine points in the first 9:36 of the fourth quarter, and a 20-2 run gave the Pistons a 112-105 lead with 2:35 left.

Brunson’s three-point play and clever reverse layup brought the Knicks within 112-110 with 1:38 to play. Towns then stole an inbounds pass from Cade Cunningham intended for Jalen Duren and was fouled on a fast-break attempt. He hit the first free throw but missed the second.

The Knicks committed a shot-clock violation with a minute left and Towns fouled out with 49.8 seconds left, sending Duren to the line. He missed the first but made the second to put Detroit up two.

Out of a timeout, the Knicks got a shot for Brunson that misfired, but Mikal Bridges (25 points) tipped it in with 35.6 seconds left to tie the score at 113.

Cunningham, who already had put up 23 points, missed on a short jumper and Josh Hart grabbed the rebound and called timeout with 20.6 seconds left, setting up the final play.

There was little doubt who would shoot it — or the result.

Brunson ran down the clock near midcourt, guarded by Thompson, and with about 11 seconds left, Bridges sprinted toward him from near the baseline as if to set a screen, but he instead ran right by them. Brunson dribbled left and then executed a crossover dribble that left Thompson moving in the wrong direction, giving Brunson the space he needed.

“Just found a way to create some separation,” he said. “Shot it a little earlier than I wanted to, but Ausar is such a great defender, man. And just the fact that I got that much space, I had to shoot it. Happy the ball went in.”

“I just know him so well and I think high-pressure situations happen that doesn’t faze him,” Bridges said. “I’ve been around him so long and he’s even-keeled throughout the whole night. Doesn’t matter if he’s struggling, no matter if he’s hooping, you can never tell. All I thought is if he can get some separation, once he got separation, I knew it was curtains. When he shot it and made it, I thought I made it because I was so geeked up. I thought I hit the game-winner. Needed that.”

The Knicks still had to survive the final possession by the Pistons, but when Anunoby finally threw the ball in the air and the horn sounded, the celebration was on.

“It’s great. It’s a great feeling,” Hart said. “Obviously we’re disappointed we couldn’t do it at home in front of our fans and that, but that’s one of the best feelings in sports, going into a hostile environment of an opposing team and silencing them.”

“Hang tough,” Knicks coach Tom Thibodeau said. “Persevere. Get through things. The playoffs is all about toughness and your discipline. There are going to be emotional highs and lows. You know all that, and you have to stay focused on the task at hand.’’