Rondo, who turned in his 13th straight game of at least 10 assists, collected his NBA-best fifth triple-double this season as the Celtics put the came away in third quarter with a 31-12 run.
Paul Pierce helped send Boston to its fifth consecutive victory with 23 points and seven rebounds.
Miami, meanwhile, continued its road struggles despite 23 points from LeBron James. The Heat lost for the seventh time in their last 10 contests away from home.
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Aaron Carter is still in love with Hilary Duff