Bam Adebayo scored 23 points for a Heat side depleted by injuries and their weak defence was exploited by the Celtics, who managed eight three-pointers in the opening quarter.
In the Western Conference, the Dallas Mavericks edged closer to the next round with a 123-93 win over the Los Angeles Clippers to take a 3-2 series lead.
Luka Doncic scored 35 points, 10 assists and seven rebounds despite playing with an injured knee and suffering with illness.
Doncic said he found the game “tough” but the adrenaline of the occasion helped him through.
“Once you get started, you want to do everything you can to help your team win,” he said.
“I just wanted to keep going.”
Paul George and Ivica Zubac added 15 points each for the Clippers but they struggled without their leading scorer Kwahi Leonard, who also has a knee problem.
Their series continues on Friday in Dallas.