Miami will attempt to finish off a series sweep when Game 4 is played in New York Sunday.
The Heat had only a two-point lead heading into the fourth period, but they outscored the Knicks 29-14 during the closing 12 minutes, with James leading the way.
James scored 32 points, hitting just 9-of-21 from the field but making 12-of-13 from the foul line.
Dwyane Wade added 20 and Mario Chalmers had 19 for the Heat. Chris Bosh, who made a quick round trip to Miami to be with his wife when she delivered a child, collected 10 rebounds to go with eight points.
Carmelo Anthony scored 22 points and kept the Knicks in the game through three quarters.
New York played without Amare Stoudemire, who suffered a lacerated hand when he hit a case containing a fire extinguisher following his team's loss in the second game of the series.
The Knicks shot a mere 31 percent for the game and made only 4-of-20 from 3-point range.