MIAMI -- 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 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. The Heat expected Boston's best -- and the Celtics didn't disappoint.

"This group had resolve," Wade said of the Celtics. "They came out and played a great game. It was physical early. They brought the game to us. That can't happen. We used our crowd and the energy to get back into the game and we had to play better."

Paul Pierce scored 21 points, Kevin Garnett added 18 and Ray Allen 13 for Boston. Rondo finished 16 of 24 from the floor, 10 of 12 from the foul line and made both his three-point tries.

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"He was absolutely phenomenal," Celtics coach Doc Rivers said. "Put us, put the whole team at times on his shoulders . . . We had a lot of opportunities to win the game."

Allen's three-pointer with 34.3 seconds left tied the game at 99. 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.

James missed two free throws 21 seconds into overtime, and Miami looked in trouble. But the Heat held on, in a game in which it took 47 free throws -- 24 by James -- to Boston's 29.

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.