The Heat took a 3-2 lead in the finals of the Eastern Conference and a win over the Pistons on Saturday in Indianapolis would set up a championship showdown against San Antonio.
Indiana took a four-point lead after the first half, during which the Pacers put themselves in position to jump in front in the series for the first time.
Roy Hibbert hit the opening basket of the third quarter to put Indiana in front by six and Miami then outscored the Pacers for the rest of the period 30-11. James scored 16 of his 30 points in the third and Udonis Haslem added 11 in the quarter.
Miami finished off the period on a 12-2 run that included a pair of 3-pointers from James and three consecutive jump shots from Haslem.
The Heat shot 51 percent for the game with James hitting 13-of-25 shots while pulling down eight rebounds and handing out six assists. Haslem missed just once in nine field goal attempts and had 16 points overall.
Miami picked up the vital victory despite off nights from Dwyane Wade and Chris Bosh, usually counted on to contribute big numbers along with James. Wade went 3-of-8 from the field and scored just 10 points in 40 minutes. Bosh had seven points.
Paul George scored 27 points and added 11 rebounds to lead the Pacers while Hibbert had 22 points.