Manish Rathore, however, exited the competition after a closely-contested loss against Rui Yamaguchi of Japan in the men’s 55kg category.
Sakshi, Lakshya and Jaismine will join fellow Indian boxers Sachin Siwach, Hitesh Gulia, Muskan, Minakshi and Sanju in the next round.
Back in April, India had won six medals at the previous World Boxing Cup leg in Brazil. The Indian women, however, did not compete in Brazil on account of the national championships.
The tournament in Astana is the second and last of two scheduled World Boxing Cup meets for the year.
Boxers accumulate ranking points through their performances at these two meets with the top pugilists qualifying for the World Boxing Cup Finals scheduled in India in November.
The Kazakhstan leg will run until July 7, with over 400 boxers from 31 countries, including Olympians, competing across 10 weight categories in both men’s and women’s divisions. India have sent a 20-member team.