The 25-year-old Australian came from behind to beat the Argentine world No.31 2-6 6-3 7-5 in two hours, six minutes.
Besides making the last eight, where he will face local favourite Luca Van Assche, he has climbed into the world's top 60 for the first time in his career.
Beginning the event in qualifying, ranked at No.83, Hijikata has beaten five higher-ranked players so far and will climb to No.48 if he does it again.
Many a tennis underdog has pulled off a shock win but, drained by the feat and the attention, they rarely back it up.
It seemed as if this would be the case with Hijikata in the French capital on Thursday when he lost the first set in 26 minutes. The new Aussie No.2 lost the first eight points and while he then held to love to get into the tie he was broken again in his third service game.
In their only previous meeting, in Hangzhou last year, Etcheverry won 6-1 6-4, and appeared on course for a similar swift passage.
But Hijikata had lost the first set to Djokovic 6-2 and, once again, he steadied himself then roared back.
The Sydneysider survived a break point in the 12-minute opening game of the second set, then broke in the fourth game. He maintained that advantage to win the set in 43 minutes and force a decider.
That went with serve until 5-5. Hijikata had to save three break points at 1-2, but his other four service matches to had all been serenely held to love. However, he had not forced a break point of his own.
Now, at the key moment, he did, and he took it. That left Hijikata serving for the match. He opened with an ace.
Etcheverry levelled to 15-all but Hijikata won the next three points to take the game, set and match, ending with an emphatic forehand smash across court.
Hijikata celebrated joyously, prompting television pundit Ryan Harrison, the American former top-40 player, to comment: "He is a guy who is typically mild-mannered, he's as fired up as I've ever seen him before."
Next up is 47-ranked Van Assche, who beat Lorenzo Musetti 7-5 3-6 6-4 in a seesaw epic that had the crowd gripped after watching two French defeats.
Hijikata has never played Van Assche and will also have to deal with a home support that helped Van Assche come back from two break points down at 3-4 in the third. He won 12 of the next 13 points to seal the match.
That came after Ben Shelton and Tommy Paul overcame home hopes to set up an all-American quarter-final. Twelfth-seed Paul saw off Quentin Halys 7-6 (7-3) 6-4 but Shelton was pushed hard by Arthur Rinderknech. The third seed eventually won 3-6 6-4 7-6 (7-5).
Earlier Carlos Alcaraz received a walkover into the quarter-finals after Matteo Berrettini withdrew from their third-round clash with an arm injury.
The match had been scheduled to headline the evening session, but the Italian world No. 43 pulled out after experiencing pain in his arm.
Second seed Alcaraz advanced directly to the last eight, where he will face Taylor Fritz who inflicted another American defeat on the hosts when he beat Arthur Fils 6-3 6-4.
In the other quarter final Portuguese lucky loser Nuno Borges, who beat Ignacio Buse 6-0 6-2, will play Casper Ruud or Jan-Lennard Struff.
with agencies
