Tenth seed Khachanov is the first Russian to reach the last eight in Paris since Mikhail Youzhny in 2010.
The 23-year-old will face Austrian fourth seed Dominic Thiem, the runner-up to Rafael Nadal in the 2018 final, for a place in the semi-finals.
"It was the best match ever for me at a Grand Slam," said Khachanov who seems to like the French capital having won the Paris Masters in the east of the city last year.
"Let's go for more."
Khachanov fired 57 winners past the two-time Roland Garros semi-finalist Del Potro with victory assuring the Russian of a first ever spot in the world top 10.