Cecchinato is the first Italian man to reach a Grand Slam semi-final since 1978 after his thrilling 6-3, 7-6 (7/4), 1-6, 7-6 (13/11) victory over the 12-time major champion.
The 25-year-old, who had never won a Grand Slam match in his career before Roland Garros, goes on to face Austrian seventh seed Thiem for a place in Sunday’s final.
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.
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.
Djokovic had also squandered three set points in the second set and failed to serve out the fourth in the ninth game after being 5-2 in front.
In an extraordinary post-match press conference, Djokovic then said he may even skip Wimbledon where he has been champion three times.
“I don’t know if I am going to play on grass,” said the Serb.
“I’m just not thinking about tennis at the moment.”
Cecchinato struggled to comprehend his triumph, coming just two years after his career was almost derailed when he became embroiled in match-fixing allegations.
“Maybe I’m sleeping. It’s amazing, it’s unbelievable for me. I’m very happy because it’s unbelievable to beat Novak Djokovic in a quarter-final at Roland Garros. It’s amazing,” he said.
Thiem reached his third successive French Open semi-final with a 6-4, 6-2, 6-1 demolition of a hobbled and exhausted Alexander Zverev who admitted he was close to quitting the tie.
German second seed Zverev simply ran out of gas, paying a heavy price for needing three successive five-set matches to reach his first Grand Slam quarter-final.
“I definitely thought about it, but I didn’t want to pull out for the first time of my career in a Grand Slam quarter-final,” said Zverev.
Thiem, who lost in the semis to Djokovic in 2016 and Nadal last year, said he is now better-equipped to go all the way.
“I’m a better player in general, for sure. There was another year of work where I improved and developed my game,” said the 24-year-old.
“I know how to handle a Grand Slam now, how… to get that deep in such a tournament, and I think everything gets better with experience.”
US Open champion Stephens brushed aside Russian Daria Kasatkina to set up a repeat of last year’s Flushing Meadows final with fellow American and good friend Keys.
The 10th seed produced a clinical performance to down Kasatkina 6-3, 6-1 on Court Philippe Chatrier, firing 17 winners.
Earlier in the day Keys, the 13th seed, reached the semi-finals for the first time by seeing off Kazakhstan’s Yulia Putintseva 7-6 (7/5), 6-4.
“I’m excited to play my good friend in the semi-finals, we’ve already played in the US Open final and it’s really good for American tennis,” said Stephens.
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.
Keys struck 30 winners past a battling Putintseva in an impressive display as she continued her recent revival on clay, having never reached the quarter-finals in Paris before this week.
The 23-year-old struggled last September under the pressure with the US Open title on the line, losing 6-3, 6-0, but she is confident that performance won’t affect the match 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.
“I obviously rely on what I learned there and how to manage my emotions and manage the moment, but there were so many late nights and I was so tired. It feels completely different here.” DM
A crevasse is in ice and a crevice is in rock. Now you know.