James had 24 points, 11 assists and nine boards to help the Heat continue their pursuit of the NBA record of 33, set by the Los Angeles Lakers in the 1971-72 season.
Jameer Nelson paced the Magic with 27 points and 12 assists.
The league's other long win streak came to an end, though, as the New Orleans Hornets saw off the Denver Nuggets 110-86.
Ryan Anderson led the Hornets with 23 points, while Danilo Gallinari scored 24 for the Nuggets.
John Wall poured in 47 points to lift the Washington Wizards to a 107-94 victory over the Memphis Grizzlies.
Wall added eight assists to his career-high points haul, while Emeka Okafor contributed 21 points and nine rebounds.
Stephen Curry had 25 points and 10 rebounds as the Golden State Warriors saw off the Los Angeles Lakers 109-103, despite 36 points from Kobe Bryant.
Elsewhere, the Indiana Pacers beat the Atlanta Hawks 100-94 and the Utah Jazz were 107-91 winners over the Philadelphia 76ers.