Geeta, who was playing in the 59-kg category for the first time, won all her bouts against her opponents from Japan, Canada, Mongolia and Belarus.
India had qualified for the first time in this eight-team event held in Ulaanbaatar, Mongolia from March 1-3.
The Indian team lost its opening Group B match against Japan 2-5, followed by another defeat by an identical margin to hosts Mongolia.
In their final match, India overhauled the Canadian challenge 4-3 to finish third from their Pool.
China won the gold medal while Mongolia and Japan settled for silver and bronze respectively.