De Minaur conducted his on-court interview all in French.
"I want to say thank you to everyone. It was an incredible atmosphere. I was not expecting to get to the quarterfinals at Roland Garros because I haven't played very well on clay in recent years," the 25-year-old said.
He tried to explain how difficult it was playing Medvedev but couldn't find the right French, saying "C'est trop difficile" (It's too difficult), and still drawing loud cheers and applause.
"It is a lot easier to just have a normal conversation instead of trying to explain tennis," de Minaur said.
"I don't have that sort of vocabulary in my disposal."
The slight Sydneysider with the big heart and electric speed was left barely able to understand that he had come from a set down to win.
"It's pretty extraordinary, if you ask me. I always thought that for me to play well on the clay I needed hot, lively conditions," said de Minaur, who had never before been past the second round at Roland Garros.
Most of all, de Minaur said, this was a victory for experience, for continually going to the well in grand slams — 27 now — and improving bit by bit each year.
"So much of grand slam tennis in my opinion is just experience, because ultimately you can put in all the work in the world — and I believe I'm one to do so — but it's how you conserve energy, how you use your energy in these long, gruelling five-set matches, that there's a lot to learn from," he said.
"And it's not just the fact that you play a gruelling match, it's how you then bounce back for the next round. That's probably what my body has now started to get used to.
"Mentally I was very calm today. I knew that there was a good chance that we could even go into a fifth set, so I was ready for anything.
Next up for de Minaur is No.4 Alexander Zverev, who went the distance with No.13 Holger Rune to win 4-6, 6-1, 5-7, 7-6 (7-2), 6-2.
Former Paris quarterfinalist Medvedev had lost only twice in eight previous meetings with de Minaur, and drew first blood with a break in the third game, but the 28-year-old was pushed hard in the next before extending his lead.
De Minaur drew loud cheers from the crowd as he retrieved shots relentlessly to mount a late comeback attempt, but Medvedev wrapped up the opening set with little fuss to briefly dampen his opponent's spirits.
Medvedev shrugged off a string of superb winners from de Minaur's racket at the start of the second set but surrendered it tamely with an unforced error after taking a medical timeout for blisters on his foot midway through.
With the momentum shifting, the 25-year-old de Minaur blazed to a 5-1 lead en route to winning the third set before he traded breaks with Medvedev early in the fourth and pulled away shortly after for a famous win.
Novak Djokovic was bothered by his right knee, then found himself down a set and a break, before doing what he does so well, coming back to beat No.23 Francisco Cerundolo 6-1, 5-7, 3-6, 7-5, 6-3 for his record 370th win in a grand slam match.
Djokovic, 37, the defending champion at Roland Garros, broke a tie with Roger Federer for the most match wins at major tournaments — and also for the most grand slam quarterfinals for a man by reaching the 59th of his career.
And the No.1-ranked Djokovic did it in ways he has so often over his years of dominance and 24 major trophies, both turning around a contest after trailing and emerging when the tension is greatest.
This victory across more than 4 1/2 hours means that Djokovic is now 40-11 in fifth sets over his career.
"I was maybe three or four points away from losing this match," Djokovic said.
For Djokovic, this was the second consecutive outing that lasted more than four hours, that he fell behind 2-1 in sets and that he won in five. In the third round, he made his way past No. 30 Lorenzo Musetti, a 22-year-old from Italy, finishing Sunday after 3am, the latest finish in French Open history.
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