In an epic fourth-set tie-break, Djokovic saved three match points but wasted three set points as Cecchinato became the lowest-ranked man to make the last four in Paris since 100th-ranked Andrei Medvedev in 1999.
Argentine Diego Schwartzman produced a remarkable fightback from two sets down to overcome South Africa's Kevin Anderson 1-6 2-6 7-5 7-6 (0) 6-2 and reach the quarter-finals.
"A hard one to swallow", a glum Djokovic acknowledged during a brief news conference, in which he delivered clipped answers and said he might not play during the upcoming grass-court season. I just came from the court.
"That's where I'm back", said the 2016 French Open champion. It's incredible. It's unbelievable for me. "It's awesome", he said.
Dominic Thiem made it to a third straight French Open semifinal after swatting aside second-seeded Alexander Zverev 6-4, 6-2, 6-1 on Tuesday. He then held three set points in the tiebreaker but couldn't convert any.
Thiem, who lost in the semis to Djokovic in 2016 and Nadal previous year, said he is now better-equipped to go all the way.
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"I knew I'm not going to win the match".
The 31-year-old Serb has reached the last eight at Roland Garros for a 12th time - an Open era record. I know him well. "It's awesome", said the 25-year-old who is the first Italian to get this far at a Slam since Corrado Barazzutti at Roland Garros in 1978.
American 13th seed Madison Keys reached the quarter-finals for the first time with a 6-1, 6-4 win over Romania's Mihaela Buzarnescu.
And moments later, in the breaker, Cecchinato took his one set point opportunity to move two sets to love up.
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. The two have only faced off once before, with Putintseva defeating Keys in 2016.
How much prize money can each player earn at Roland Garros?
"Honestly, the (US) Open feels like it was 12 years ago at this point", said Keys, who is yet to drop a set in the tournament.
Cecchinato and Djokovic know each other well: They have practiced together in Monte Carlo, where Cecchinato trains at a tennis academy and Djokovic has a home. "It feels completely different here".