James' points total was a season high for the Heat, who notched their 16th consecutive home win. The Miami superstar also had six rebounds, four assists and three steals.
Mario Chalmers supplied 19 points, six boards and four assists for Miami.
The Heat won despite the absence of Dwyane Wade, who missed the contest with a sore left knee.
Evan Turner scored 26 points to go with eight rebounds for the 76ers, who fell 1 1/2 games behind Boston in the race for the Atlantic Division top spot.