But five years to the day after the Celtics snapped Houston's 22-game streak, the Heat extended theirs to 23.
"It means a lot," James said. "I know the history of the game. To be sitting in second place right now ... for us to be there and doing it the way we want to do it, it means a lot."
James added 12 assists and Mario Chalmers scored 21 for Miami.
"I believed we were going to win the game before the game. I thought we were going to win the game during the game. And I thought we should have won the game," Celtics coach Doc Rivers said. "I give them credit. They made some spectacular plays."
The Heat had not won in Boston since the New Big Three was formed — including that double-overtime loss on Jan. 27, when former Celtic Ray Allen returned with his new team.
That was the day Rajon Rondo was diagnosed with an ACL tear that ended his season. This time, it was Garnett who sat out, though Rivers said he would have played if the thigh injury had not been compounded by the flu.
"It was the best team in the league and we took them to the breaking point," Green said. "We've just got to, when Kevin comes back, continue to play like we did today."
Green had 14 points in the first quarter, when the Celtics scored the last 17 to open a 31-19 lead. Boston led by as many as 17 in the second, but Miami went on a 15-6 run just before the half to make it a six-point game and then scored the first eight points in the third quarter to take the lead.
Green had 12 in the second quarter and 12 in the third.
But the Heat still pushed their winning streak to 23.
"No moral victories," Pierce said, "even though it was a close game."
Notes: Miami's win and Atlanta's loss on Monday night clinched the Southeast Division for the Heat. ... Pierce committed seven of the Celtics' 20 turnovers. ... James was called for a technical foul for taunting when he stood over Jason Terry after a dunk. It was James' sixth technical of the season and 39th of his career.