In the quarterfinal match, the Russian beat her compatriot Veronika Kudermetova.
The meeting ended with a score of 6:4, 7:6 (7:5).
The duration of the game was 2 hours 9 minutes.
Kasatkina converted five break points out of 17, made three double faults and did not make a single ace.
Kudermetova filed right through three times, made two errors on the pitch and converted four out of seven break points.
In the semi-final, Kasatkina will play with the winner of the pair Iga Svintok (Poland) - Jessica Pegula (USA).
Earlier, the President of the Russian Tennis Federation Shamil Tarpishchev spoke about Kasatkina's game at Roland Garros.