NEW YORK — Amare Stoudemire sat through the sluggish start, and had one thought in mind when it was his turn to change it.

“Dominate,” he said. “Dominate is the main objective. That’s the only thought that I think when I go in the game.”

That’s exactly what Knicks did. Really, really dominate.

Stoudemire was 10-for-10 from the field for 21 points, and New York unleashed a 38-4 run on Sacramento in the first half and clobbered the Kings 120-81 on Saturday night for its fourth straight victory.

DeMarcus Cousins had 25 points and nine rebounds for the Kings, who were horrible from all areas of the court, missing shots right at the rim on offense and often not even getting anywhere near the Knicks’ 3-point shooters on defense.

“It’s crazy. I don’t know what happened, man,” said guard Tyreke Evans, who shot 3-of-10 for seven points. “We missed a lot of layups. I missed a lot of layups. One of those nights. I think it was the worst game I ever played in the NBA. I can’t explain it.”

The Knicks were down 13-3 and in the midst of a 1-for-13 shooting start when Stoudemire checked in. The Kings got the lead to 18-6, but then Stoudemire had a dunk and three-point play on consecutive possessions, scoring seven points in a 19-4 burst to end the quarter that gave the Knicks a 25-22 lead.

New York then went on to challenge the franchise-record victory margin of 48 points and kept alive Mike Woodson’s chances of coaching the Eastern Conference All-Star team.

It was an awesome display by New York in front of some special guests: 150 children, their families and teachers from Sandy Hook Elementary School. The Knicks didn’t even need much from leading scorer Carmelo Anthony, who tied a season low with nine points and had his run of 20-point games snapped at 31, the longest single-season streak in franchise history.

“(Saturday) it was just one of those games where (we) tried to find it elsewhere,” Anthony said. “You know, scoring there, we didn’t need my scoring (Saturday). Everybody contributed from that aspect of it.”

J.R. Smith scored 25 points and Steve Novak added 15 as the Knicks made 19 3-pointers. Tyson Chandler had 11 points and 20 rebounds, becoming the first Knicks player with consecutive 20-board games since Marcus Camby on Dec. 8 and 11, 2001.

“We had a slow start and then it’s like as soon as a couple of guys started hitting shots, it’s contagious,” Novak said. “I think it was just crazy how quickly it turned once we started making shots.”

But the story was Stoudemire, a former All-Star who missed the first 30 games after knee surgery and has served as a reserve since his return. He changed the game with his energy and scoring after the Knicks sleepwalked through the start, and finished one basket shy of tying the team record for field goals without a miss, held by Johnny Newman and Bernard King.

Feeling back to 100 percent and showing off some of his old explosiveness, Stoudemire could feel the game change when he went in.

“It feels great to provide a certain amount of energy to get us over the hump,” he said.

Stoudemire made the first basket of the second quarter, kicking off a 19-0 run. Novak’s third 3-pointer of the period made it 44-22 with 7:06 remaining, about 40 seconds after Stoudemire exited to a loud ovation.

Marcus Thornton ended Sacramento’s drought, but Novak hit another 3 to start a run of eight straight points as the Knicks extended it to 52-25.

Stoudemire was 6-for-6 for 13 points in the half as the Knicks led 56-33. He was 9-of-9 after three, when the Knicks led by 45, and made a jumper in the fourth before leaving for good to more cheers.

He struggled with injuries last season and critics continue to insist he, Anthony and Chandler can’t play well together. Yet Stoudemire remains very popular with fans, who remember that he was the big star willing to take on the rebuilding project in the summer of 2010 and has been willing to come off the bench now.

Anthony passed 17,000 points for his career but took only 12 shots, yet the Knicks still led by as much as 50. Sacramento coach Keith Smart didn’t think the Knicks were trying to embarrass his team.

“I don’t feel that way. Those guys are pros,” Smart said. “Sometimes guys that don’t get the opportunity to play, they get on the floor, they’re going to play. You can’t tell them to run the shot clock down and feel sorry for that team over there. These are pros.”

Woodson said he already has plans to be someplace warm during All-Star weekend, but those plans may have to be altered. The coaches whose teams have the best winning percentage through Sunday’s games earn the All-Star nods, and the Knicks would be a half-game ahead of Miami if the Heat lose in Toronto on Sunday afternoon.

“If it’s meant to be, it’s going to happen,” Woodson said.

At 30-15, the Knicks have 30 wins before the break for the first time since the 1996-97 season, when they were 32-13 after 45 games.

“We felt like we had a great team, a team with a lot of possibilities in training camp and we have to stick by it,” Chandler said. “It’s a long journey for us but we have the potential to be special.”

Notes: Children from the Newtown, Conn. choir sang the national anthem before the game as the Knicks welcomed the big group from Sandy Hook Elementary School. The Knicks organization on Tuesday visited Newtown, where 20 children and six adults were shot and killed at the school in December. The team hosted the “Knicks Family Fun Day” for 400 children and their families at Newtown Youth Academy. “They got hit hard and they’re still trying to recover from it. So to be able to go down and touch those kids and talk to parents, and them being able to come up here and watch us play, I think it’s pretty special,” Woodson said. “I don’t care what community you live in or where you go and visit, man, you hate to see a community going through something like that, especially when you’re dealing with young kids. A lot of those kids never had a chance.”

Tyreke Evans, Iman Shumpert

Sacramento’s Tyreke Evans (13) fouls New York’s Iman Shumpert during the Kings’ 120-81 road loss to the Knicks. AP photo

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