Kudermetova in the first round defeated her compatriot Oksana Selekhmetyeva in three sets with a score of 4: 6, 7: 6 (7: 3), 6: 4.
The game lasted 2 hours and 20 minutes.
Simona Halep will become Kudermetova's next rival.
The tennis player from Romania is the winner of Roland Garros (2018) and Wimbledon (2019).
The prize fund of the Kremlin Cup is about $ 565 thousand.
Earlier it was reported that the Russians Karen Khachanov and Andrei Rublev made their way to the quarterfinals of the doubles competition at the Kremlin Cup in tennis.