MIAMI (AP) — The biggest postseason comeback in Miami Heat franchise history wasn’t enough.

The Heat needed more — and got it, digging deep to take a 2-0 lead in the Eastern Conference finals.

LeBron James scored 34 points and grabbed 10 rebounds, Dwyane Wade scored 23 and the Heat rallied from 15 down to beat the Boston Celtics 115-111 in overtime on Wednesday night.

Mario Chalmers scored 22 for the Heat, who won despite an unbelievable night by Rajon Rondo. The Celtics guard played all 53 minutes and scored 44 points, dished out 10 assists and grabbed eight rebounds.

Paul Pierce scored 21 points, Kevin Garnett added 18 and Ray Allen 13 for Boston.

Allen’s 3-pointer with 34.3 seconds left tied the game at 99-all. James missed two shots, first a layup — he got the rebound of his own miss — and then a jumper on the final possession of regulation, and to overtime they went.

Game 3 is Friday in Boston.

The Heat had come back from 14 points down in playoff games twice before, first in Game 6 of the 2006 NBA finals — their title clincher — and again last season against Philadelphia.

And this one was slipping away, more than once. James also two free throws 21 seconds into overtime, and Miami looked in trouble.

The scoring dossier in overtime began like this: Rondo scored, Heat tied it, Rondo scored, Heat tied it, Rondo scored, Heat tied it.

When Rondo missed a layup with 1:33 left, Miami took advantage, with Udonis Haslem getting a dunk to put the Heat up 105-103. And after a turnover on the next Boston possession, Wade drove the lane, hit the deck and watched as his layup bounced on the rim and dropped through.

Garnett stood over Wade and glared, to no avail. Wade hit the free throw, and Miami was up 110-105 with 59.7 seconds left.

On a night where the Heat missed 16 free throws — including at least four by James in crucial situations — they would survive.

Miami was down by 15 in the first half and by as many as 11 in the third quarter, before a pair of 3-pointers by James started a comeback. Wade made consecutive jumpers midway through the third to shake off a slow start to his night and get the Heat within three both times, and the 2006 NBA finals MVP set up Haslem for a three-point play with 2:55 left that gave Miami its first lead since the opening minutes, 73-71.

As Haslem’s shot dropped, Wade spun at midcourt and punched the air. More highlights followed.

Miami’s lead got to as much as seven in the third after James blocked Pierce’s shot near the rim, sending the ball high into the air and starting a sequence that was capped by a three-point play from Wade, pushing the margin to 78-71. It capped a 12-0 run for the Heat, who took an 81-75 lead into the fourth.

It was the fifth straight game where Miami outscored its opponent by double-digits in the third quarter. In each of the previous four of those outings, Miami never trailed in the final period.

That streak ended in this one.

And a call that Boston argued against played a big role in the Celtics getting the lead back.

James stole the ball from Rondo early in the fourth, drove down the court and got wrapped up by Mickael Pietrus, who was assessed a clear-path foul, meaning Miami got two free throws and the ball. James missed both foul shots, Mike Miller missed a 3-pointer later in the possession, and the lead stayed at 85-81.

Barely a minute later, it was gone. Pietrus hit a 3-pointer, Rondo followed with a steal and layup and Boston led 86-85. The Celtics led by five with 3:50 left after a jumper by Pierce, and the Celtics looked to be in control.

It was temporary. The Heat scored the next nine points, Haslem’s jumper with 1:08 remaining put Miami up 98-94. So of course, back came Boston — Allen’s 3-pointer tying the game a few moments after Pierce fouled out.

Early on, it was all Boston. Over the first 15-plus minutes, Boston was shooting 65 percent (15 for 23), Miami 27 percent (7 for 26).

Miami’s point guard did his best to keep the Heat close.

Chalmers had 12 in the second quarter and seven in a 14-6 Miami spurt to end the half. He hit a pair of 3-pointers during the flurry, Wade got his first points of the night on a falling-down layup with 27 seconds left and the Heat closed the margin to 53-46 by halftime.

NOTES: Celebrities in attendance included UCLA coach Ben Howland, rapper Flo Rida and former Dolphins quarterback Dan Marino, a regular in the Heat crowd. … Rondo’s other 22-point first half was Feb. 22, 2009 at Phoenix. … Allen, considered one of the game’s absolute best shooters for many years, said he’s been getting plenty of unsolicited advice lately on how to get rolling again. “I’ve only been doing this for 20 years,” Allen said at the morning shootaround. … Haslem (6) had more rebounds than Boston (5) in the third quarter. … Heat C Ronny Turiaf started, played the first 4:51 and did not return. Joel Anthony started the second half in Turiaf’s place.