Daria Kasatkina advanced to the final four for the first time in her 26th appearance at a major after defeating Kudermetova.
In a match that lasted over four hours, the king of clay beat Novak Djokovic in a performance that simply defies logic.
The German won the tie 6-4, 6-4, 4-6, 7-6 (9-7) in three hours and eight minutes of adrenaline fueled tennis.
Camila Giorgi defeated Zhang Shuai and Yulia Putintseva in the first round before knocking out No. 7 seed Aryna Sabalenka.
Djokovic and Nadal met in the semi-final of the competition last year, which saw the Serb emerge victorious after an epic battle.
Nadal came into the French Open with little experience on clay, having only played five matches on the surface this year.
Djokovic was aiming to keep his perfect record against the Argentine, but as he went out of the tunnel onto the court, he discovered that not was on the same page.
Gauff will play fellow countrywoman Sloane Stephens in a major for the second time in a year.
The King of Clay advanced to the quarter-final where he will face world no. 1 Novak Djokovic, who beat Diego Schwartzman in straight-sets.
US tennis player and 11th seed Jessica Pegula emerged victorious in her third round match against Tamara Zidansek.