James piled up 30 points to warm up for their next game, which comes against the Oklahoma City Thunder in a reprise of last year's NBA finals series.
He has now scored at least 20 points in all 24 Heat games this season, matching the longest run of 20-plus efforts to start a campaign since Karl Malone did it for Utah in 1989-90.
Dwyane Wade added 21 points and seven assists as the Heat rode the strength of a big third quarter to beat Utah, going on a 22-6 run to open the second half.
Marvin Williams scored 16 for Utah, which played the second half without Mo Williams, who appeared to hurt his right thumb early in the game.
The Memphis Grizzlies slipped half a game behind San Antonio in the Southwest Division despite having a better winning percentage, owing to the peculiarities of the standings, after a 121-96 loss at Houston.
The Grizzlies entered the game allowing an NBA-low 89.2 points a game. But they had no answer for James Harden, who scored all of his 31 points in the first three quarters and reached at least 20 points for an eighth straight game. Jeremy Lin added 15 points and 11 assists.
Houston used a big run midway through the second quarter to take the lead, and didn't trail after the break, winning their 13th straight home game against Memphis.
Mike Conley had 16 points for the Grizzlies on a night when leading scorer Rudy Gay finished with a season-low six points.
And the Los Angeles Lakers came from 14 points down in the fourth quarter to force overtime and beat the Warriors 118-115.
Kobe Bryant had 34 points and 10 rebounds, while Steve Nash finished with 12 points and nine assists in his first game in almost two months.
The 38-year-old Nash came back from 24 games out with a small fracture in his lower left leg and made only his second appearance for the Lakers. He converted a step-back shot for the final points in overtime to lift Los Angeles to its fourth straight victory.
Jarrett Jack scored 29 points in a disappointing collapse for Golden State, which had won 11 of 14 games to get off to its best start in 20 years.