- World number one Halep, the runner-up in 2014 and 2017, survived a first round scare to defeat America's Alison Riske but has been in cruise control ever since, happily going under the radar to make the quarter-finals.
Another rain delay sent the players off court and shortly afterwards play was suspended for the day.
Rafael Nadal improved to 11-0 in French Open semifinals. "Nadal's capable of keeping this very aggressive, high-intensity level over an unbelievably long period of time".
Play has resumed at the French Open after a suspension due to rain of about 55 minutes. It is his best result at Roland Garros since 2009 when he also made the semi-finals losing to Roger Federer in five sets.
Second-seeded pairing Latisha Chan of Taiwan and Ivan Dodig of Croatia have won the French Open mixed doubles title for the first time.
During the changeover after the set, a trainer came out to tape both of left-handed Nadal's wrists.
He fired long on a first set point, Nadal saved the second with a jaw-dropping drop shot but on the third, just after the match was interrupted for a few minutes while an unwell spectator was evacuated, Schwartzman unleashed a stunning forehand victor down the line - his 20th victor.
Now comes what del Potro called "the challenge that every player wants to have" - taking on Nadal at Roland Garros.
And on the penultimate point of the semifinal, after being run ragged, the 2009 US Open victor could only offer up a smile.
Nevertheless, Cecchinato can look back on a breakthrough tournament - he had never won a match at a grand slam before beating Marius Copil 10-8 in the fifth set last week.
Women's semifinals: No. 1 Simona Halep beat No. 3 Garbine Muguruza 6-1, 6-4.
Surely, so did del Potro. "His game is too good for me". It's just how it's happened for me", Stephens said, "I think once I get going in a tournament, I'm pretty consistent, which is good.
Backed by fans who loudly chanted her first name between games, Halep went ahead 3-0 with the help of only one victor.
The 21-year-old Nadal became the first man since Bjorn Borg in 1980 to win three successive titles at Roland Garros.
He has lost just twice in 87 singles matches at the French Open. In fact, plenty would claim him top-three at this point.
The key moment, though, was the gripping second-set tiebreak. Thiem won 76 percent of his total service points and saved five of his six break points. And he did just that, easier opponent notwithstanding, with a 7-5, 7-6 (12/10), 6-1 win.
Cecchinato, whose career was nearly derailed two years ago by a match-fixing scandal before his name was cleared, stopped the rot in the sixth game.
That put Thiem, a 24-year-old from Austria who is seeded No. 7, in the semifinals at the French Open for the third consecutive year. Get ready for an 11-time champion. Of her first 14 points, 13 arrived via errors by Muguruza - nine unforced, four forced.
Muguruza raced to a 4-0 lead and never looked back. Nadal had more trouble with another Argentine, the diminutive Diego Schwartzman, in the quarterfinals.