Allen's three-pointer with 34.3 seconds left in the fourth quarter 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.
"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."
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 the Sixers.
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 when Miami missed 16 free throws - including at least four by James in crucial situations - it 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 threes 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 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.
* David Stern wants to take a closer look at flopping and for referees to be able to take a second look at all flagrant fouls. And the NBA commissioner isn't sure he wants to see his veteran players in the Olympics anymore.
Stern and deputy commissioner Adam Silver said Wednesday the league is committed to sending top players to the Olympics only through London, and then wants to look into saving them just for the world basketball championship and having the Olympics reserved for those 23 and under, as soccer does. That discussion will happen later with FIBA, basketball's world governing body.