LeBron James had 31 points and 12 rebounds and Dwyane Wade scored 23 points as host Miami advanced to the NBA Finals for the second straight season.
Chris Bosh added 19 points on 8-of-10 shooting for Miami, which dominated the final eight minutes en route to winning the final two games of the Eastern Conference finals.
Rajon Rondo had a triple-double with 22 points, 10 rebounds and 14 assists and Paul Pierce scored 19 points for Boston.
Miami opens play in the NBA Finals against Western Conference champion Oklahoma City Thunder on Tuesday in Oklahoma City. The Heat lost in six games to the Dallas Mavericks in the 2011 finals.
The tightly contested Game 7 featured 20 lead changes until Miami caught fire with an 18-4 spurt to turn a one-point deficit into a 99-86 lead.
James began the decisive surge with a dunk and he drained a 31-foot 3-pointer to get the lead to 88-82 with just under seven minutes to play. Wade had a run of five straight points, including a three-point play to give Miami a 98-86 advantage with 2:53 to play.
James hit one of two free throws with 1:23 left to culminate the onslaught.
Rondo had 10 points in the third quarter in a contest that was knotted at 73 entering the final quarter. Boston’s last lead came on Ray Allen’s 3-pointer to make it 82-81 with 8:49 to play.
The Celtics led 59-51 after Rondo’s basket with 9:26 left in the third quarter before Miami scored eight straight points to tie the contest. Wade’s hoop with 5:45 left in the stanza represented the Heat’s first lead since less than five minutes into the contest.
Shane Battier added 12 points on four 3-pointers for the Heat.
Brandon Bass had 14 of his 16 points in the first half for Boston, which also received 15 points from Allen and 14 points from Kevin Garnett.
Boston led by as many as 11 points in the first half lead before the Heat closed the gap to 53-46 at halftime.
GAME NOTEBOOK: James had five games of 30 or more points and 10 or more rebounds in the series. … Rondo has 10 career playoff triple-doubles. … Bosh played 31 minutes and drained three 3-pointers in his third game since returning from a lower abdominal strain. … Bass had four of Boston’s 10 steals. … Miami committed only three of its 13 turnovers in the second half. … Boston was 7-for-18 from the field in the final quarter.