The 26-year-old Muscovite in the opening match of the tournament defeated Nuno Borges from Portugal in four sets with a score of 6:3, 2:6, 6:4, 6:4.
The game lasted 2 hours and 26 minutes.
The Russian received the 21st seed from the organizers of the competition.
The Portuguese made it to the main draw of the tournament through qualification
Khachanov's next opponent will be Hugo Delien from Bolivia.
The prize fund of the tournament is more than €43 million.
Earlier, Andrey Kuznetsov lost to Diego Schwartzman in the first round of Roland Garros.