The Heat's franchise-record winning streak was extended thanks to a driving layup from James and Miami then survived a missed 3-point attempt by Arron Afflalo at the buzzer.
Orlando took a three-point lead with 1:36 to play on a jumper by Jameer Nelson, but the Magic could not score again.
Chris Bosh brought Miami with a point by making two free throws with 38 seconds to go and Orlando then missed two chances to extend the lead. Dwyane Wade blocked one of those chances on a shot by DeQuan Jones with 21 seconds to play and Al Harrington failed to convert a 3-point try with 13 seconds remaining.
James made 7-of-14 from the field and 11-of-12 from the foul line. Wade added 24 points and Bosh had 17 points along with 10 rebounds.
Nikola Vucevic scored 25 points to lead Orlando, which made 17 fewer free throws than did Miami.