updated 1:21 a.m. ET May 29, 2008

BOSTON - Boston’s three All-Stars finally put it all together to move the Celtics one win away from the NBA finals for the first time since the original Big Three’s heyday.

Ray Allen scored 29, hitting a long 2-pointer with a minute left after Detroit came within one point, then he and Kevin Garnett each made a pair of free throws down the stretch as the Celtics beat the Detroit Pistons 106-102 in Game 5 of the Eastern Conference finals on Wednesday night.

Boston will take a 3-2 lead into Game 6 on Friday in Detroit. With a victory there or on Sunday back in Boston, the Celtics would advance to the NBA finals for the first time since Larry Bird, Kevin McHale and Robert Parish took them there in 1987.

“We knew the significance of this game,” said Garnett, whose 33 points were his most in the playoffs this year. “You don’t win this game, you put basically yourself in a corner. ... They’re experienced, and they’ve been in a lot of pressure situations. Now it’s up to us to go up there and try to get one.”

Kendrick Perkins had career playoff highs with 18 points and 16 rebounds, and Rajon Rondo added seven points, 13 assists, six rebounds and four steals for Boston. Paul Pierce scored 13 of his 16 points in the first half, when Perkins outrebounded the Pistons 13-11 by himself.

“Perkins is eating us up,” Pistons coach Flip Saunders said.

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The 6-foot-10 center, in his first playoffs as a starter, helped Boston to a 42-25 rebounding edge in the game. Although he’s just 23, he knows that players such as Garnett, Pierce and Allen can’t afford to let this chance at a title get away.

“I know our Big Three veteran guys. I know this opportunity doesn’t come much,” he said. “I knew if I was up in age, up in my 30s, and a young fellow was there I’d want him to go all-out for me, too.”

The 29 points was also a playoff high for Allen, the usually reliable scorer who had been cold for most of the playoffs.

“My feeling right now is no different than if I scored 10 points and we won the game. It’s a great feeling,” Allen said. “Just winning gives me the greatest joy, regardless of what I’ve done.”

Chauncey Billups scored 26 and Richard Hamilton had 25 points for Detroit, which has reached the conference finals six consecutive years but played for the championship just twice and won once in that span.

“The good thing about it is we’re going home,” said Billups, who twice drove to the basket in the final 10 seconds, hoping for a foul that wasn’t there, and also missed an inconsequential 3-pointer at the buzzer. “We’ve been here before, and we don’t like being in this position, but we’ve fought hard.”

Hamilton strained his right elbow in the final seconds. X-rays were negative.

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