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.
"We look forward to the next challenge," James said. "Still one more step."
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 Dwyane Wade and Chris Bosh in Miami.
The Heat reached last year's NBA Finals but lost to the Dallas Mavericks.
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.
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.
Source: AFP Global Edition