BOSTON -- The Miami Heat’s Big Three passionately want to win an NBA title – or seven. LeBron James left home to do it. Dwyane Wade sacrificed money. Chris Bosh relinquished big fish status.

But no one can underestimate the desire of Boston’s Big Three. Like the Heat, Kevin Garnett, Ray Allen and Paul Pierce forged an alliance in order to win championships. They got one in their first season together four years ago and none since.

Which team has a greater sense of urgency?

On Sunday, it was the Celtics for the second consecutive game competing as if they had synchronized their internal clocks and could hear the tick-tock getting louder and louder.

Heat players heard their own clock, an alarm clock that jolted them out of a defensive slumber in the second half as they raced back from 18 points behind to salvage the game and send it into overtime.

But the Celtics outleaned the Heat 93-91 at the finish line to tie their Eastern Conference finals series 2-2 and guarantee they will return to rowdy TD Garden for Game 6.

As in Game 2, Miami had a chance to win in regulation but after James elected not to drive to the basket, Udonis Haslem missed a poor last-second jump shot as James did last week. Pierce fouled out, again, then James fouled out for the first time as a Heat player – at a most inopportune moment – with 1:51 left in overtime.

“It was like chess,” Allen said. “They took our queen, then we took their queen.”

With both teams’ leaders reduced to observers, Boston clung to a 92-91 lead. Mickael Pietrus grabbed two offensive rebounds off missed three-pointers but Boston still couldn’t score, giving the Heat another chance to take the lead. But Shane Battier missed a three and Haslem committed an offensive foul, which led to Rajon Rondo taking two free throws. He sank one.

With 14 seconds left, Miami primed for its final shot. Yet another opportunity to get a step closer to that championship. Tick tock. Wade, dribbling on the perimeter, pump-faked Marquis Daniels into midair. Daniels twisted to avoid fouling Wade, opening an unobstructed look at a three-point winner.

Wade missed, and clenched his fists and teeth in frustration.

“No one said this would be easy,” Heat coach Erik Spoelstra said. “We had a couple of real good opportunities.”

The Heat can’t dwell on those blown opportunities, not when the Celtics smell doubt.

The Heat was on the brink of breaking the Celtics’ will with a second overtime heartbreaker. They put the dagger in but couldn’t twist it.

Last season in Game 4, the Heat clawed out of an 11-point hole in Boston to wrest the series away from the Celtics and won in five. For awhile it looked like déjà vu.

But the Heat was too hesitant in overtime, scored a meager two points on 1-for-8 shooting and got outrebounded 6-3 – that’s a hustle stat. Boston didn’t do much better, but its four points were enough. That’s all Boston’s aging stars need – enough.

Miami won the first game of this series with ease, regrouped to win the second in overtime and was steamrolled early in the last two. Is this a case of the tide turning or simply the home team absorbing the energy of its fans? We will find out more Tuesday in Miami.

On Sunday, Garnett, 36, Allen, 36, and Pierce, 34, looked exactly like they were collaborating on their 90th playoff game with cunning facilitator Rondo. Garnett played vintage KG basketball, dominating the boards, blocking five shots and mixing bruising layups with soft jumpers. Allen looked springy on his four three-pointers despite the bone spur floating around inside his ankle. Rondo dished exquisite assists, including a perfect lob and a pinpoint bounce pass. Pierce renewed his fierce rivalry with James and they accumulated 12 fouls.