Underdogs Miami, who suffered a 20-point thrashing in the first game of the series, recovered to earn a 111-101 road victory.
The Heat torched the Celtics with 23 three-pointers – two shy of the NBA play-off record.
“Everybody came to play,” said Tyler Herro, who led the Heat with 24 points.
“We lost bad in game one and everybody responded. That’s all you can ask for from a group of guys.”
Herro sank six three-pointers and added 14 assists, with all fiveHeat starters posting double-digit points.
Miami are without star wing Jimmy Butler and starter Terry Rozier through injury and, after Sunday’s 114-94 defeat, many thought the Celtics would wrap up a four-game sweep.
“We understood how many missed opportunities we had hesitating to shoot the threes in game one, and we had the mentality coming in of just let it fly,” said Caleb Martin, who added 21 points.
“We were hungry. The only way you beat a team like that is to come in and try to play on the same level.”
Boston’s Jaylen Brown scored a game-high 33 points while Jayson Tatum finished with 28 points, but the Celtics were limited to 12 three-pointers from 32 attempts.
The best-of-seven series moves to Miami for the third game on Saturday.
Elsewhere on Thursday, the Oklahoma City Thunder claimed a commanding 2-0 lead in their Western Conference play-off series against the New Orleans Pelicans.
Shai Gilgeous-Alexander produced his best-ever scoring total in a post-season game, scoring 33 points as the Thunder cruised to an emphatic 124-92 victory.
Game three is on Saturday in New Orleans.