Miami won its sixth straight and handed the Jazz only their second loss in 10 games.
Utah held a one-point lead heading into the fourth quarter but Miami opened the period on a 15-4 run.
James had nine assists with seven rebounds while Dwyane Wade added 28 points. Zydrunas Ilgauskas had 16 points and 10 rebounds.
Al Jefferson led the Jazz with 25 points and 11 rebounds. Deron Williams had 21 points and 12 assists.
Utah made just 1-of-14 attempts from 3-point range.