LeBron James scored 31 points and grabbed 12 rebounds to power Miami over Boston 101-88 and give the Heat a berth against the Oklahoma City Thunder in the NBA Finals.
Dwyane Wade added 23 points and Chris Bosh contributed 19 as, together with James, the Heat's "Big Three" scored all 28 of Miami's points in the fourth quarter, which began with the Celtics and Heat deadlocked at 73-73.
Miami took the best-of-seven Eastern Conference championship series four games to three to reach the NBA Finals, which will start on Tuesday in Oklahoma City. The Thunder beat the San Antonio Spurs in the Western Conference final.
"It was good to see us come together in a very competitive series and I have great respect for the championship DNA they (Celtics) have," said Heat coach Erik Spoelstra. "We do not take this for granted. I am happy we got through this. Obviously we have a bigger goal in the next round."
The Heat and Thunder split two regular-season meetings.
Boston led early in the fourth quarter before James, Bosh and Wade seized command with a 20-6 run.
James kept alive his hopes of capturing his first NBA title, his main goal when he departed the Cleveland Cavaliers in 2010 to join fellow superstars Wade and Bosh in Miami.
The Heat reached last year's NBA Finals but lost to the Dallas Mavericks.
"It has been a long 12 months," Wade said. "When you lose in the final it hurts. But you can't forget it. You try to get back to this moment so you can redeem yourself and succeed."
Rajon Rondo led Boston with 22 points, 14 assists and 10 rebounds. Paul Pierce added 19 while Ray Allen scored 15 points and Kevin Garnett contributed 14 points.
"This is the worst feeling we feel in our lives and our careers," said Allen. "One team wins that last game. We have been through a lot. We won a lot of games up to this point and we fought hard to keep it together.
"There are so many emotions now. This one hit me hard. We wanted it so bad."
An early 9-0 Celtics run gave Boston a 19-12 lead and the Celtics led 27-23 after the first quarter and 53-46 at half-time.
"We wanted to keep going and they might get tired," Wade said. "Tonight we made the plays and the shots to put us over the hump."
Brandon Bass, playing a key role with Garnett on the bench in foul trouble, led Boston with 14 first-half points and the Celtics were aided by 10 Heat turnovers in the first half. Bass finished with 16 points.
But Miami battled back in the third quarter, an 8-0 run early in the second half helping them pull even entering the fourth quarter.
Bosh finished the game with a trio of three pointers. His third three-point shot gave the Heat an 86-82 lead.
"For two years he has been our most important player because he makes it all work," Spoelstra said of Bosh.
Spoelstra said they are looking forward to the challenge of playing the Thunder in the finals.
"We have been through a lot," Spoelstra said. "We think the adversity has strengthened our core, built our character. There is no question we will need it in the next round."