Kostevych, the world champion, had started the finals in eighth place after a disappointing qualifying round before steadily working her way towards the top of the field in the finals.
She moved into the lead on the penultimate shot but was caught again by Sekaric, who had the best qualifying round, on the final round, forcing the one-shot shoot-off.
Maria Grozdeva of Bulgaria also showed nerves of steel by winning the bronze medal following a shoot-off for third place with China's Ren Jie.
