BOSTON — The Knicks’ best chance of upsetting the Celtics may have come and gone last night with a flick of Ray Allen’s wrist and a bad step by Chauncey Billups.
The Knicks imposed their will on the ragged Celtics for much of the night, beating them at their own grinding game, building a 12-point halftime lead and leading by three with 37.8 seconds left.
But it ended in a nightmare for Carmelo Anthony and the Knicks.
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Allen fired in a 3-pointer over Ronny Turiaf with 11.6 seconds from the left wing and Anthony ended a wretched second half by front-rimming a potential last-second, game-winning trey as the Knicks suffered a 87-85 Game 1 heartbreaker at TD Garden.
The Knicks broke their seven-year playoff drought, yet failed to break their 10-year drought without a playoff win. But they came close. Darn close.
Whether they remain competitive the rest of the first-round series is uncertain, after point guard Billups sustained a strained left knee with just under a minute remaining when his leg buckled on a drive. He did not return, and his status for Game 2 — and the rest of the series — is unknown.
Billups, who aggravated the knee against the Bulls on Tuesday, wore a knee brace during practices leading up to Game 1. He initially hurt the knee compensating for the left thigh bruise he suffered in March.
After the game, Billups was limping and said, “I really don’t have a clue” on whether he will be ready for Game 2 tomorrow night.
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Anthony, in his Knicks’ playoff debut, sputtered badly in the second half in a game in which he was saddled with foul trouble after picking up two infractions in the first 1:28.
Anthony finished with 15 points on 5-of-18 shooting, scoring just three in the second half on 1-of-11 from the field. He also committed five turnovers.
It was a shame Anthony could not find his second-half rhythm as it wasted a spirited defensive effort and a big game from Amar’e Stoudemire, who shut up trash-talking Glen “Big Baby” Davis with 28 points on 12-of-18 shooting and 11 rebounds.
Afterward, Anthony was undaunted.
“I’m [still] excited about the series — it came down to a Ray Allen 3, he made a big play, I had a chance to make a three and I missed it,” Anthony said. “They didn’t do nothing special. They won a Game 1 on their home court, which is what they’re supposed to do, and we got another shot at it. We’re very confident. We’re going to look at this game and build off it. We feel we have a chance to win Game 2.”
After Allen drilled the dagger, coach Mike D’Antoni did not have any timeouts left. Trailing by two, the Knicks raced the ball upcourt. Anthony got it at the right wing and lined up an open look, but the shot hit the front of the rim. Kevin Garnett grabbed the rebound and win.
“I missed shots I normally make,” Anthony said. “I’m not too concerned about my individual performance. We did some things great for most of the game.”
Coach Doc Rivers said the Celtics messed up on the Knicks’ final possession by not fouling though they had a foul to give.
“We kind of screwed up,” Rivers said. “We wanted to foul them at midcourt. Because when it left Carmelo’s hands, I was thinking, ‘Wow.’ We got away with it.”
In another huge blow, Anthony was called for an offensive foul before Allen’s dagger with 21 seconds left, when he and Paul Pierce got entangled and Anthony pushed off. Anthony argued all the way to the bench after the Celtics called timeout. D’Antoni was ticked.
“In my eyes, obviously I’m biased, I thought it was a tough call,” D’Antoni said. “It’s going to be a dogfight, but we have to make plays down the stretch.”
Allen finished with a team-high 24 points, but it was Garnett’s alley-oop slam off an inbounds with 37.3 seconds left that led to the Knicks’ demise. Toney Douglas, making his playoff debut, banged in a 3-pointer from the left wing with 37.8 seconds left, giving the Knicks an 85-82 lead.
Rajon Rondo lofted the pass for Garnett, who was freed on a back pick, for the slam, cutting the deficit to 85-84.
“It surprised me,” Turiaf admitted.
“We just didn’t communicate real well on that,” D’Antoni said.
Despite losing Anthony for nearly the entire first quarter, the Knicks held down the Celtics in the first half, taking a 51-39 halftime lead and briefly quieting Causeway Street, which grew louder as the night wore on.
marc.berman@nypost.com