The 27-year-old James, still seeking his first championship in his ninth NBA season, was aided by Dwyane Wade's 19 points and Mario Chalmers' 11 as the Heat notched their fourth straight post-season victory.
Miami also played tough defense, forcing 24 Knicks turnovers while holding New York to 35.7 shooting from the field in the initial contest of their Eastern Conference semifinal series.
J.R. Smith netted 17 points for New York, which committed 26 fouls.
Carmelo Anthony managed only 11 points on 3-of-15 shooting from the floor for the Knicks.
Swim Week Miami Beach 2014 [PHOTOS]