He cruised through the first set, held his nerve in the second set tiebreak, survived a comeback from former world number one Djokovic in the third, before prevailing in a highly-entertaining fourth-set tiebreak.
The 31-year-old, victor of the tournament on the iconic red clay in the French capital in 2016, booked his place in the last 16 with a 6-4, 6-7, 7-6, 6-2 win in a match which lasted 12 minutes shy of four hours.
"I was two breaks down on the tie-breaker and I had two or three match points and then on the fourth one I was very exhausted".
In a roller-coaster of a quarter-final, both men were warned for coaching, 2016 champion Djokovic required two medical timeouts while the Italian was docked a point for unsportsmanlike behaviour.
"In the most important moments I managed to play an extra shot in the court, made him run and made him uncomfortable".
His climb up the rankings and his efforts here are all the more remarkable given what happened to him in 2016, when he was embroiled in a match-fixing scandal in Italy.
"It was an wonderful, high level match", said Zverev.
But he has never reached a Grand Slam quarter-final, although the longer best-of-five format has worked twice in his favour now at Roland Garros. "It's fantastic", he said.
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Keys, the US Open runner-up a year ago, will face either Czech 26th seed Barbora Strycova or Yulia Putintseva, the 98th-ranked Kazakh, for a place in the semi-finals.
Yet Djokovic won the third set at a canter, and a suddenly frustrated Cecchinato was hit with a point penalty for unsportsmanlike conduct. This will be Zverev's first quarterfinal match in a Grand Slam, so Thiem edges him in experience.
"It was the best moment of my life", Cecchinato said. How hard is it to accept defeat in such good grace in the same manner as you can accept victory?
'I need to - I don't know. Stephens, last season's US Open champ, is in the midst of a rebound after getting bounced in the first round of this year's Australian Open.
The 10th seed produced a clinical performance to down Kasatkina 6-3, 6-1 on Court Philippe Chatrier, firing 17 winners. Thiem is 4-2 against Zverev so far in their careers, but Zverev has won two of the last three.
"How? I mean, we'll figure [it out]".
The 25-year-old, who was ranked 957 just six weeks before her maiden Grand Slam triumph last year after a series of injury problems, is now into the last four of a major for the third time.
From that point there was no way back for the Spaniard, who was aiming to reach his first Roland Garros quarter-final at the 15th attempt.