James scored 39 points, hitting 14-of-18 from the field.
The Heat needed James' hot shooting to maintain their perfect record over Dallas since losing to the Mavericks in the 2011 NBA Finals.
Dallas closed within a point with 2:33 to play on a jump shot by Dirk Nowitzki, but Miami finished off the game with solid free throw shooting to pick up its second straight win and its fifth in six games.
Dwyane Wade scored 17 points and had eight of Miami's 19 steals. Nowitzki scored 28 points to lead the Mavericks.