MIAMI — It wasn’t merely that three-point beauty, the sweet shot Boston Celtics forward Paul Pierce launched defiantly over the outstretched hand of LeBron James that hit nothing but net with just less than a minute remaining Tuesday night.

The game wasn’t decided on James’s missed jumper seconds before, or Mario Chalmers’s misfire with just more than 40 seconds to play, or Dwyane Wade’s miss with five seconds left.

The Celtics leaned on a host of players and seized nearly every critical moment to cobble together an excruciatingly hard-fought 94-90 victory, which gave them a 3-2 lead in the Eastern Conference finals while pushing the Miami Heat to the brink of elimination.

Even after Pierce’s three-pointer gave the Celtics a four-point lead with 52.9 seconds left and silenced the American Airlines Arena crowd, the game didn’t feel secure until Ray Allen and Kevin Garnett each made two free throws in the final seconds.

“I asked a lot of our guys — maybe too much, honestly, at times — and they came through,” Boston Coach Doc Rivers said. “We just hung around long enough to get to the fourth quarter.”

The crushing defeat left the Heat, which has lost three straight games in the series after taking a 2-0 lead, in jeopardy of getting knocked from the playoffs Thursday in Boston. The Heat must hope for a Game 7 on Saturday in Miami for any hope of returning to the NBA Finals in consecutive seasons.

“It’s not going to be easy,” said Miami forward Chris Bosh, who returned to action and scored nine points after having missed nine playoff games because of an abdominal strain. “It’s going to be an extremely difficult time. . . . I think we’re in the biggest challenge of our lives right now, of our professional careers.”

Miami was led by 30 points from James, who also grabbed 13 rebounds, and 27 from Wade, as the Heat shot just 39 percent from the field.

Throughout Tuesday’s rugged contest, the Celtics didn’t rely on any one player. Not their aging Big Three, or even their slithering star, Rajon Rondo. They depended on a whole bunch of guys for critical shots and critical stops.

Garnett overcame a slow start to score 26 points on a night when Rondo scored only seven on 3-of-15 shooting from the field. Rondo rolled up 13 assists, however, as five Celtics scored in double figures. Pierce got 19; Brandon Bass, 10; Ray Allen, 13; and Mickael Pietrus — who hit two late three-pointers — tallied 13.

“We wouldn’t be in this situation, up 3-2, if it wasn’t for our entire team,” Rondo said.

Heat Coach Erik Spoelstra sounded uncustomarily defensive during his postgame meeting with members of the media. He said the Heat would look forward to Thursday’s game and not back at the last three, all of which have been close and not one of which has seen Miami stand up and make key late shots.

 “Okay, it’s a loss, and that’s all it is,” he said. “What our focus is right now is to fight any kind of noise from the outside, or any human condition, and to collectively come together strong to prepare for the next game.”

The Heat led by 13 in the first half and nine in the third quarter, but Boston got late excellence from Garnett, who scored 18 points after halftime, and key shots from Rondo, Pietrus and Pierce.

Though Boston entered the fourth quarter leading, 65-60, Miami retook the lead with a dominant stretch. Norris Cole stripped Rondo in the open court early in the period, taking the ball the other way for a possession that resulted in a basket by Wade off an offensive rebound. A layup, steal and three-point shot by James after that vaulted the Heat on top, 74-72.

But then Rondo, who had missed nine of his first 10 shots, woke up, hitting back-to-back field goals, and Garnett swished a wide-open jumper with 2 minutes 54 seconds left to put Boston up, 81-80. The Heat got buckets from Chalmers and Wade, but the three-pointers by Pietrus and Pierce put the game out of reach.

“We played hard,” James said. “Everytime we got them down, they made runs. They made us stagnant offensively and got stops that got them back into the game.”

Bosh, who hadn’t played since the first game of the Heat’s second-round series against the Indiana Pacers, returned midway through the first quarter Tuesday, and gave the Heat an unexpectedly forceful boost in a surprisingly complete performance. Bosh, however, did not play late in the game.

He tallied nine points and seven rebounds during three separate stretches and 14 minutes of play. Spoelstra said he did not think it would have been fair to ask Bosh to handle late duty after such a long absence.

“I definitely have more to give, and I’ll be there,” said Bosh, who did not play in the fourth quarter. “When the time comes again, I’ll definitely be ready to play more than I played tonight.”

The Heat’s third-leading scorer during the season, Bosh had been missed during this series for his inside presence, mainly against Garnett. But as Boston used an 20-9 run to help overcome a 13-point second quarter deficit, Garnett had his way with Bosh inside, scoring six straight points to bring Boston to within two, 40-38.

Garnett continued the domination into the third quarter, making Udonis Haslem look small and ineffective. Garnett hit back-to-back dunks, one on an alley-oop pass from Rondo, and on his way to 10 third-quarter points. A Keyon Dooling three-point shot with two seconds remaining in the third quarter lifted the Celtics to a 65- 60 lead entering the final period.

“It was just a matter of time,” Rondo said. “We kept fighting and we found a way to get the win.”