Rondo's running jumper with 2:32 remaining put the Celtics ahead for good at 92-91, and after Miami's Shane Battier missed a 3-point try with 24 seconds left, the Boston guard hit 1-of-2 free throws for a two-point lead.
The Heat's Dwyane Wade had the last shot of the game but missed a 25-foot, 3-point attempt, allowing the Celtics to hang on and even the best-of-seven series at two wins apiece.
Rondo finished with 15 assists while Paul Pierce scored 23 points before fouling out for the Celtics.
LeBron James poured in 29 points, including a score-tying 3-pointer late in regulation, and Wade ended with 20 points, seven rebounds and six assists for Miami.
The Heat will try to retake the advantage when the series returns to Miami for Tuesday's Game 5.
Notable deaths of 2014 [PHOTOS]
UPI Sports Results for September 19, 2014