James went 12-of-17 from the free-throw line while Dwyane Wade added 23 points, six rebounds and six assists for the Heat, who rebounded from a 3-games-to-2 deficit to defeat the Celtics in Game 7 of the Eastern Conference finals.
They now advance to their second NBA finals in two years, and will travel to Oklahoma City to take on the Western Conference champion Thunder starting Tuesday.
Chris Bosh, playing in his third game since returning from an abdominal injury, went 8-for-10 from the floor en route to 19 points -- including eight in the decisive fourth quarter -- and hauled down eight rebounds off the bench for Miami.
Rajon Rondo notched a triple-double with 22 points, 14 assists and 10 boards, while Paul Pierce added 19 points for the Celtics, who fell in the post-season to Miami for the second straight year.
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