The Celtics outscored the Heat 31-12 in the third quarter, turning a 49-44 halftime lead into an 80-56 advantage. They stayed ahead by at least 19 the rest of the way for their fifth straight win.
Miami's last three losses have been by at least 15 points and its previous worst defeat of the season came just one week earlier in a 103-87 setback at Oklahoma City.
Rondo finished with 16 points, 14 assists and 11 rebounds, reaching the triple-double mark with 8 1/2 minutes to play. It was his 13th consecutive game with at least 10 assists and his fifth triple-double of the season.
The Celtics, combining tenacious defense with outstanding play in transition, increased their Atlantic Division lead to one game over idle Philadelphia.
The Heat, playing their third game in four days, were led by LeBron James with 23 points but he had no assists for only the second time in his career. Dwyane Wade added 15 points. The Heat continued to struggle on the road, losing for the seventh time in their last 10 games away from home. Miami has the fewest home losses in the league at 21-2 but is only 16-12 on the road.
Paul Pierce scored 23 points, and Brandon Bass added 16 points and 10 rebounds for Boston.
Miami scored two of the first three baskets of the third quarter, cutting the lead to 51-48. Then the Celtics outscored the Heat 29-8 the rest of the period, hitting 14 of 23 shots while Miami made only 5 of 19. Rondo had eight assists in the quarter.
It was 55-50 when Rondo's layup began a 17-2 run in which the Heat's only points were two free throws by Wade. James finally hit a field goal, making it 72-54, but the Celtics scored eight of the remaining 10 points in the quarter.
The Celtics led 29-19 after one, led by Rondo's 10 points, four rebounds and four assists. They stretched that to 34-23, then went cold offensively while the Heat scored the next 10 points, closing the gap to 34-33.
Bass stopped the drought with a shot from the top of the key with 4:57 left in the first half, Boston's first points in 4:08.
With the score tied at 40, the Celtics got the next five points on a jumper by Kevin Garnett and a three-point play from Pierce to take a five-point lead.