Despite an error when she two-footed a double loop in her combination jump the teenager improved her free skate score by a massive 18 points to take a third title in Sochi for hosts Russia.
Both Kim and Kostner gave error-free performances.
"I just have faith that the judges made the right decision," said former world champion Kostner.
Kim had been bidding to become just the third woman to win back-to-back titles after Norway's Sonja Henie, triple winner between 1928 and 1936, and Germany's Katarina Witt in 1984 and 1988.
Kim watched in tears as the scores came up putting her second behind four-time Russian national champion Sotnikova, who finished runner-up at the Europeans behind countrywoman Julia Lipnitskaia last month.
Lipnitskaia, 15, finished fifth on Thursday after she fell on a triple Salchow jump.
Sotnikova landed seven triples including a triple Lutz-triple toeloop to score 149.95 points for her skate to "Introduction and Rondo Capriccioso" for an overall 224.59 points.
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