Miami turned a four-point lead at intermission into a double-digit cushion by scoring the first eight points of the third quarter helped by a pair of three-pointers by Shane Battier.
The lead was stretched to 20 points but Utah battled back to close the gap, getting as close as eight in the fourth quarter, though the Heat were never seriously threatened.
The Heat won every quarter, building their lead behind the all-round brilliance of James and an equally well-rounded effort by his running mate Dwyane Wade to lift Miami's record to 18-6, and push past the fast-starting New York Knicks (19-7).
James shared the team lead with nine rebounds and seven assists, while Wade scored 21 points to go with seven rebounds and seven assists.
Miami shot a blistering 52 percent from the floor, including 11-for-24 from three-point range in improving to 13-2 on their home court.
The Jazz, who were paced by Marvin Williams with 16 points, continued their road struggles, falling to 5-12 away from home.
James has scored at least 20 points in all 24 Heat games this season, matching the longest such streak to start a season since former Utah Jazz forward Karl Malone in the 1989-90 campaign.
Miami, winners of four straight games, will put their streak on the line on Christmas against the Western Conference-leading Oklahoma City Thunder (21-5) in a rematch of last season's NBA Finals.
(Reporting by Larry Fine in New York; Editing by Ian Ransom)