Kim, who has twice won the world title, received a score of 74.64 to hold a narrow lead over Adelina Sotnikova of Russia and Carolina Kostner of Italy.
The top seven skaters at the end of the short program were within 14 points of each other and any could win the gold medal on Thursday with a dazzling free skate.
Sotnikova received 74.64 points for her routine and Kostner was awarded 74.12 points.
Gracie Gold of the United States finished fourth, Yulia Lipnitskaya of Russia was fifth and Americans Ashley Wagner and Polina Edmonds were sixth and seventh.
Mao Asada of Japan, who finished second to Kim at the Vancouver Olympics, had a flawed program that left her in 16th place.
Swim Week Miami Beach 2014 [PHOTOS]