The Jazz, playing the second half without point guard Mo Williams, cut it to 10, and were back within 10 in the final minutes of the fourth before back-to-back 3-pointers by LeBron James and Mike Miller capped a 14-0 run.
Williams missed the second half with a sprained right thumb. Results of an X-ray were negative.
There was no miracle comeback for the Jazz, like the last time they were in Miami in Novermber 2010. That year, Paul Millsap score a career-high 46 points, including 3-pointers in the final minutes of regulation.
James scored 30 points and flirted with a triple-double, adding nine rebounds and seven assists. He scored more than 20 points for the 24th game, becoming the first player to do so in the first 24 games of a season since Karl Malone in 1989-90.
Marvin Williams scored 16 points to lead the Jazz, but 12 of those came in the first quarter and the first-year Jazz small forward was held to 27 minutes.
The Jazz head to Orlando for Sunday's game against the Magic to wrap up a four-game road trip.