The 26-year-old tennis player from Vladikavkaz defeated British Jack Draper in the third round match.
An athlete from Great Britain, with a score of 6:3 4:6, 6:5 in favor of the Russian, refused to continue the fight due to injury.
The game lasted 2 hours and 23 minutes.
Khachanov's next opponent will be the winner of the match Alex de Minor (Australia) - Pablo Carreno-Busta (Spain).
The total prize fund of the tournament is over $60 million.
Earlier, Russian Ekaterina Alexandrova was unable to qualify for the third round of the US Open.