Annu achieved the mark in her first attempt as she led the field for a while before being overtaken by China's Li Zhang and Lingwei Li, who won gold and silver respectively.
Annu's first attempt proved to be her best as her later attempts were far below than the first. However, she bettered her own record of 58.83m, which she had set in June this year during the National championship in Lucknow.
Zhang Li set the Asian Games record with her best throw of 65.47, which she achieved in her sixth and final attempt.
The Chinese bettered the Games 61.56m mark, set by Japan's Yuki Ebihara at the 2010 Guangzhou Games. Ebihara (58.72) finished fourth behind Annu. Lingwei took silver with a throw of 61.43m, which she managed in her fifth attempt.