James grabbed eight rebounds and dished off seven assists for the Heat, who broke open a close game with a 33-5 run beginning late in the third quarter and stretching into the final frame.
Ray Allen came off the bench to drain a trio of 3-pointers en route to 13 points while Chris Bosh (12 points, 10 rebounds, four assists) and Dwyane Wade (10, six assists) also reached double figures as Miami bounced back from a 92-88 loss in Game 1.
The Heat trailed 62-61 with 3:15 left in the third quarter when Chalmers made a driving layup and converted a foul shot, putting Miami ahead for good. Another Chalmers 3-point play as the quarter ended added momentum.
James connected on a 16-footer to open the fourth quarter and the Heat rolled from there.
Danny Green provided 17 points for San Antonio, whose seven-game post-season winning streak came to an end.
The Spurs will attempt to regain the advantage when the finals shift to San Antonio for Tuesday's Game 3.