Four-time NBA Most Valuable Player James connected on 16-of-23 shots from the field, including 4-of-8 from 3-point range, and added nine rebounds and six assists for Miami.
Vince Carter’s free throw with 7:47 remaining gave the Mavericks a 95-92 lead but the Heat scored the next 14 points to seize command.
James opened the run with back-to-back 3-pointers, added a basket and two free throws for 10 points in the run and Dallas came no closer than eight points the rest of the way.
Miami improved to 4-1 on a road trip that ends Thursday against NBA scoring leader Kevin Durant and the Oklahoma City Thunder, who ripped the Heat earlier this season at Miami.
Chris Bosh scored 22 points and Chris Andersen contributed 18 more off the bench for Miami. Dwyane Wade had 13 points and seven assists for the Heat.
German star Dirk Nowitzki led Dallas with 22 points and also contributed nine rebounds and seven assists for the Mavericks, who won six of their past seven games.