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Tom Thibodeau and his players don’t need any Christmas presents this year.

They gave themselves and their fans the best gift of all Monday.

A victory over the title-contending Bucks.

The Knicks saved their finest performance of the season for this holiday showcase, snapping their nine-game losing streak to Milwaukee at a sold-out Garden.

Two days after Giannis Antetokounmpo, Damian Lillard and the Bucks torched the Knicks at MSG, the home team returned the favor in an impressive 129-122 victory in which the big four of Jalen Brunson, Julius Randle, RJ Barrett and Immanuel Quickley were all at the top of their game and the Knicks’ defense limited one of the league’s premier offenses.

“We played with extra energy, extra effort, obviously we made a lot more shots than we did last game. I did,” said Barrett, who had 21 points on 8 of 14 shooting after just 13 points on 5 of 17 Saturday. “Just the energy and fight. We lost to them three times already, so to come in today on Christmas to get this one feels extra sweet.”

Knicks guard Jalen Brunson #11 reacts after hitting a shot during the first quarter. Charles Wenzelberg / New York Post

The Knicks’ foursome combined for 103 points, with Brunson leading the way with 38 points, six assists and no turnovers, and the Knicks (17-12) finally contained Milwaukee from deep.

In the first three games between the teams this season, the Bucks shot 54.1 percent from 3 and averaged 19.7 made 3’s while piling up 128.7 points per game.

This encounter was different. While Lillard, Antetokounmpo and Khris Middelton had 88 between them, their teammates struggled.

Knicks center Isaiah Hartenstein #55 slam the ball during the third quarter. Charles Wenzelberg / New York Post

The rest of the Bucks shot 12 of 29 from the field and Milwaukee made only 13 of 42 from downtown.

“I just think today we needed to be a little more physical with everything we do,” Brunson said. “We needed to be more intense, our closeouts needed to be better, our running out to people at the line needed to be better, communication, everything. I think that took a step in the right direction today. We made them miss, but I think we can do a better job doing that as well.”

The Knicks beat the Bucks (22-8) for the first time since Nov. 5, 2021 — ending a nine-game skid against Milwaukee — and the victory marked their first win over one of the Eastern Conference’s two powers, the Celtics and Bucks, in seven tries.

Knicks guard Josh Hart #3 puts up a shot as Milwaukee Bucks forward Bobby Portis #9 defends. Charles Wenzelberg / New York Post

They led by as many as 16 in the fourth quarter, although it did get down to six late.

Brunson’s jumper in the lane with 1:11 left pushed the lead back to eight and he punctuated the basket with a fist pump, a rare show of emotion.

“[It meant] a lot, just because obviously we struggled against this team throughout this year, so the fact that we came up with a win today, it’s special,” Brunson said. “I liked the way we had a lead and no matter how much they cut the lead down we stayed poised and figured out a way to keep it.”

Randle had 24 points and nine rebounds, Barrett snapped out of a recent shooting slump and Quickley had 20 off the bench.

Bucks forward Giannis Antetokounmpo #34 looks to put up a shot between New York Knicks guard Josh Hart #3 and New York Knicks forward Taj Gibson. Charles Wenzelberg / New York Post

Josh Hart was terrific at both ends in notching 10 points, nine rebounds and four assists.

Isaiah Hartenstein added 11 points, eight rebounds and four assists, and Taj Gibson chipped in three rebounds, three blocks and three assists in 15 valuable minutes.

Down 11 at halftime, the Bucks came out strong after the break.

nicks’ Julius Randle (30), center, puts up a shot during the first half of an NBA basketball game against the Milwaukee Bucks. AP

Fueled by a 12-point third quarter from Lillard, Milwaukee crept to within four on the strength of a 9-0 run. Brunson didn’t let them get closer.

He stopped the spurt with a three-point play, then scored again on a pull-up jumper and the Knicks closed the period well, maintaining the 11-point edge they had at the break.

Hart and Quickley were instrumental in the lead ballooning to 16 and Brunson ensured the Bucks never really threatened in the final minutes.

Knicks guard RJ Barrett (9) drives to the basket as Milwaukee Bucks guard Pat Connaughton (24) defends. USA TODAY Sports via Reuters Con

“They came out and played like they had practiced and we talked about it,” said Lillard, who scored 32 points. “They played faster, they played with a lot of energy and I thought they had more collective effort as well.”

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