Then Carmelo Anthony had one last chance to win it for the New York Knicks.
Allen hit a go-ahead 3-pointer with 12 seconds left off a pass from Paul Pierce and Anthony misfired on his long try at the other end, giving the Celtics an 87-85 comeback victory over the Knicks in their playoff opener on Sunday night.
"Ray's the hero with the shot," Boston coach Doc Rivers said. "Paul's the hero with the pass. That's a great example of not playing hero basketball, just trusting what we drew up. And he made the shot."
Allen led the Celtics with 24 points and Pierce added 18 to go along with solid defense on Anthony. Kevin Garnett had 15 points and 13 rebounds, and clamped down on Amare Stoudemire down the stretch.
Stoudemire had 28 points and 11 rebounds for New York, and Anthony finished with 15.
"It's all about our defense and execution down the stretch," Pierce said. "We can't rest on this victory because by no means was this our best basketball."
New York may have lost more than a game. Point guard Chauncey Billups left with 51 seconds remaining, and doctors told him the injury was a strained left knee or thigh muscle.
"I went to the basket and, as I took off on my leg it just kind of buckled on me," said Billups, who doesn't know if he will be available for Game 2 of the best-of-seven series Tuesday night in Boston. "I'm in a lot of pain right now, but that's to be expected."
New York led 85-84 before Anthony was called for an offensive foul for pushing Pierce with 21 seconds remaining.
"What I thought and what they called were two different things," Anthony said.
"Heck of a call to make," he said, "but it was the right call."
Rajon Rondo then lined up to inbound the ball but called timeout. The next time, Allen inbounded from just in front of the half-court line on the right side. He threw the ball to Pierce, then circled to the other side of the court, caught Pierce's pass and fired up the deciding basket.
"We've run that play many times," Allen said. "It's a play that has so many options and tonight I was just the option."
Allen snapped Reggie Miller's NBA record of 2,560 3-pointers on Feb. 10 in a loss to the Los Angeles Lakers on the same court where he came through on Sunday.
The Knicks then rushed downcourt and Anthony missed for the 10th time in 11 second-half shots. The Celtics got the rebound, the buzzer sounded and Rivers high-fived fans as he headed for the locker room.
Anthony and Stoudemire were options on the final play, but it was Anthony who got open.
"We've got to find a way to win down the stretch," Stoudemire said. "We had a great chance to win. We played well throughout the full 48 minutes. We just didn't quite close it out."
New York had the same problem against Boston on Dec. 15, when Pierce hit a jumper with .4 seconds left to put the Celtics ahead 118-116 at Madison Square Garden. Stoudemire then sank a 3-pointer, but it was waved off after officials determined that time had run out.
Third-seeded Boston got a tough challenge from the Knicks, who allowed 105.7 points per game during the regular season, third-most in the league.
With the score tied at 82, Toney Douglas hit a 3-pointer to put the Knicks in front with 38 seconds to go. The Celtics called timeout and immediately scored when Rondo tossed an alley-oop to Garnett on the inbounds pass.
"We just didn't communicate real well on that," New York coach Mike D'Antoni said.
The Celtics, who won their NBA-high 17th championship in 2008, are aiming to return to the finals after losing in seven games last year to the Los Angeles Lakers.
The Knicks, in the playoffs for the first time in seven years, have lost their last three postseason series and have gone 10 years without a win in a playoff game.
Boston trailed 51-39 at halftime but rallied to take a 66-64 lead early in the fourth. Stoudemire then scored 12 of the Knicks' next 18 points to power them to an 82-78 lead with 2:46 remaining.
Pierce followed with a 15-foot fallaway and Jermaine O'Neal scored on a putback, tying it with 1:12 to play.
It was a rough night for Anthony from the start. He picked up two quick fouls and went scoreless in the first quarter, but ended the half with 12 points.
The Celtics played without center Shaquille O'Neal, who also is expected to miss Game 2 with a sore right calf. O'Neal, a key to their interior defense, missed 27 games with a sore right leg. He returned on April 4 against Detroit, but quickly left again with the calf problem. He sat out the remaining six games of the regular season.
This program aired on April 18, 2011. The audio for this program is not available.