Tomljanovic cruises through in Moscow
Ajla Tomljanovic cruised past Liudmilla Samsonova claiming a 6-2 6-4 victory in Moscow to set up a last-16 clash with top seed Aryna Sabalenka, who is ranked second in the world.
World number 28 Kasatkina, who has won four WTA Tour titles, fell on home soil to Kalinina as the Ukrainian triumphed 6-2 6-3 on Tuesday (AEDT)
Anna Kalinskaya joins Tomljanovic in the next round as she defeated Dayana Yastremska 7-6 (7-5) 6-4 on home soil and the Russian will now face French and US Open semi-finalist Maria Sakkari.
Lesia Tsurenko had no issues against China's Qinwen Zheng as she won 6-4 6-3, while American Bernarda Pera beat Aleksandra Krunic 7-6 (7-3) 6-3 to seal her second-round berth.
Meanwhile, number two seed Zidansek, who sits 33rd in the world rankings, crashed out in Tenerife as world number 108 Jaqueline Cristian succeeded 7-5 4-6 6-1.
Zhang Shuai was the sixth favourite in Spain but she lost to fellow Chinese star Wang Xinyu 6-2 6-1, with Anna Karolina Schmiedlova also defeating Kaja Juvan 4-6 6-1 6-4 and Irina-Camelia Begu overcoming Marta Kostyuk 6-4 6-4.