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 per cent 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.
Kobe Bryant scored six of his 34 points in overtime as the Los Angeles Lakers stormed from behind to beat the Golden State Warriors 118-115.
The Lakers trailed by 14 at the start of the fourth, but they roared back to force the extra period and Bryant, who also grabbed 10 rebounds, brought them home.
Al Horford paced Atlanta with 20 points as all five Hawks starters hit double figures in a 92-75 win over the Chicago Bulls.
Horford also added 10 rebounds for his 13th double-double of the season.
Damian Lillard scored 25 points to help the Portland Trail Blazers stretch their winning streak to five by edging out the Phoenix Suns 96-93.
JJ Hickson also shone for Portland with 19 points and 15 rebounds.
David West led the Indiana Pacers to an unlikely comeback win as they made light of a 22-point deficit to beat the New Orleans Hornets 81-75.
The Hornets led 46-24 at one point but West's 25 points ensured the Pacers powered back and the Hornets lost for the 11th game in a row.
The Charlotte Bobcats fell to their 15th consecutive defeat, losing 110-88 to the Denver Nuggets, while the Washington Wizards lost their seventh straight for a league-worst 3-22 with Charlie Villanueva scoring 19 points in a 96-97 win for the Detroit Pistons.
James Harden led the Houston Rockets to their third straight win with 31 points in a 121-96 victory over the Memphis Grizzlies, while the Cleveland Cavaliers were 94-82 winners over the Milwaukee Bucks.
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