New York — New York’s once faint, nearly unrealistic playoff hopes have become a real possibility. The Knicks intend to seize the opportunity and run with it.

“We know what we want,” Carmelo Anthony said.

J.R. Smith had 24 points, eight rebounds and six assists, Anthony added 23 points and 10 rebounds, and the Knicks beat the city rival Brooklyn Nets 110-81 Wednesday night to move percentage points ahead of Atlanta for the eighth and final Eastern Conference playoff spot.

The Knicks were 21-40 on March 3 after a seven-game skid and are still just 33-43. But they know that record gets wiped away if they can finish off this turnaround.

“We want to get there. That’s the goal,” Anthony said. “Despite this emotional season, this up-and-down season, I think it would be a big deal to get in that spot.”

Tim Hardaway Jr. scored 17 points a game after spraining his right ankle to help the Knicks win for the 12th time in 15 games, dominating a team that had the best record in the Eastern Conference since the new year. New York won its third straight.

The Knicks made 24 of 36 shots in taking a 63-38 halftime lead in front of new president Phil Jackson, who wouldn’t have much to fix if they looked like this more often. They finished at a season-high 60 percent and outrebounded Brooklyn 41-23.

“Our guys are hungry,” Knicks coach Mike Woodson said. “Normally anybody that comes off the West Coast, when you’ve been out there for a while, that game coming back is normally a tough game, but our guys came out with energy and came out ready to play.”

Joe Johnson scored 16 points for the Nets, who had won three straight. A night after clinching a playoff berth by beating Houston, they were out of the game by the opening minutes of the second quarter.

“It was very frustrating the way we got blown out,” Johnson said. “For whatever reason, we had a few guys fighting and a few guys who wasn’t fighting. If we’re not all on the same page, you get a lopsided score like that.”

In a game that both clubs need for different reasons, the Knicks were the more desperate team, taking a 2-1 lead in the season series. None of the games has been close, but both have bigger concerns than city bragging rights, anyway.

The Knicks have almost no margin for error in a final seven-game stretch against playoff-bound opponents. They had no problem with the first one and will face the Nets one more time on April 15 on the second-to-last night of the season.

Brooklyn is hoping for home-court advantage in the first round, but fell 2 ½ games behind Toronto and Chicago for a spot.

The Nets led 20-19 late in the first quarter, but Anthony had two baskets, Smith made a 3-pointer and found Hardaway for another at the buzzer as the Knicks scored the final 10 points for a 29-20 lead.

Hardaway made another 3 to open the second and Iman Shumpert scored to make it a 15-0 run and give the Knicks a 34-20 advantage. Anthony had the first six points of an 8-0 burst that pushed it to 58-34 with 1:36 remaining in the half, and it was 63-38 at the break.

The Nets were angry with the officiating, with Johnson picking up a technical foul at halftime and coach Jason Kidd’s assistants stepped in front of him as he tried to yell toward the refs.

Brooklyn got within 14 with 2 minutes left in the third, but the Knicks, unveiling a small lineup that had Anthony as its center, stretched their lead to 82-61 heading to the fourth.

“They were the better team tonight,” Kidd said. “Lose by one, lose by 100, it’s just a loss. We move on.”

Knicks guard Raymond Felton went the locker room early in the third quarter with bruised ribs and back after a hard landing while trying to grab an offensive rebound, but was able to return early in the fourth.

• The Nets had won two in a row at Madison Square Garden. ... On World Autism Awareness Day, the Knicks honored Tarrytown, N.Y., educator Virginia Campbell with this month’s Sweetwater Clifton “City Spirit” Award for her more than 18 years teaching and helping more than 100 autistic children. The award is named for Nat “Sweetwater” Clifton, the first African-American to play for the Knicks. ... Referee Dick Bavetta was honored before working his 2,633rd consecutive game assignment, an ironman streak even longer than the one compiled by baseball Hall of Famer Cal Ripken Jr.