Rishika beat Turkmenistan's Anastasiya Prenko 6-3 6-3 in the first round.
Rishika had an all-win day as she also advanced to the doubles quarter-finals along with partner Nova Patel as they beat compatriots and wild card entrants Vaniya Dangwal and Smriti Joon 6-2 6-1 in the opener.
Zainab lost her singles match 3-6 3-6 to fifth seed Italian S Scimone but later partnering Ratnika Batra made the doubles quarter-finals.
They beat compatriots Shweta Rana and Prarthana G. Thombare 6-3 7-5.
Hence it was all over for Shweta as she lost her singles 4-6 1-6 to Nalborska Joanna of Poland.
Also advancing in the doubles was third seed Indian pair of Aishwarya Agrawal and Ankita Raina, who outplayed compatriots Shruti Archita and Sahan Shetty 6-2 6-0.
Gopika Kapoor, teaming up with South African Tegan Edwards spanked the Indian pair of Tarrannum Handa and Shreya Pasricha 6-0 6-2.
Rutuja Bhosale and Sowjanya Bavisetti went down fighting 1-6 6-3 5-10 to fourth seed Chinese pair of Sirui He and Zhaoxuan Yang.
Another Indian making exit was Ashvarya Shrivastava, who along with Korean partner Jung-Yoon Shin lost 2-6 2-6 to second seed Korean team of Kim Ju-Eun and Kim Hae-Sung.
Deccan Herald is on WhatsApp Channels| Join now for Breaking News & Editor's Picks