15th-ranked Khachanov dropped just one set in his wins over wildcard Arthur Gea and 36-year-old Marco Trungelliti to set up a meeting with 106th-ranked Dutchman De Jong, who closed the curtain on Stan Wawrinka's French Open career in the first round and outclassed Federico Cina in under two hours.
De Jong, who'd never beaten a top-15 opponent on the ATP Tour, asserted dominance on his service game early on, with the Dutchman winning a staggering 95% (19/20) of first service points in the opening set.
The 106th-ranked De Jong committed just five unforced errors, fended off two break points from the big Russian, and sealed a sensational set win with a line shot in a strong rally.
Khachanov kept chasing De Jong and nearly caught the Dutchman in the latter's second service game, which lacked the quality from his first set. Despite four break chances, though, De Jong held on.
The underdog kept this going in an equally thrilling ninth game, fending off two break points by the skin of his teeth to stay in control.
The Russian turned the tide not much later, breaking De Jong for the first time on Friday to take a 6-5 lead. Khachanov took his opportunity on the first time of asking, tying the match at one apiece.
De Jong used the second set blow as fuel and improved on his formidable opener with another showpiece - the Dutchman went 13/13 on first serve and allowed just three return points as he closed the third set out at 6-2 to move within one set of the fourth round.
In a potentially match-clinching fourth, De Jong opened furiously as he broke Khachanov on his first opportunity and hit a near-perfect game with four aces in the very next game to go up 3-0 in devastating fashion.
The Dutchman kept up his excellent service game as he fended off another break point from Khachanov to move within one game of the match.
However, on serve, De Jong dropped a double fault to initially lose the initiative in the final moments, while Khachanov recovered with an excellent winner to keep himself alive and eventually break De Jong to get things back on serve.
The unseeded player responded perfectly, holding serve and then forcing two match points at 6-5, but the Russian saved them before comfortably winning the tiebreak to take things into a decider.
With all the momentum with Khachanov and De Jong tasked with bouncing back from a huge mental blow, the seeded player entered the final set as the favourite, but the underdog responded remarkably, breaking serve twice to race into a 4-0 lead.
This time around, he kept his cool, finally prevailing 7-5, 5-7, 6-2, 6-7, 6-2 to claim the biggest win of his career.