The two remaining men's quarterfinals were suspended in progress and will resume Thursday.
On the other hand, del Potro also was involved in a rain-marred quarter-final against third seed Marin Cilic over the last two days.
But those are not quite the same as the French Open, where Nadal is 86-2 for his career.
Nadal had a brief moment of weakness in the first set, when the 24-year-old Austrian broke him in the third game.
Rafael Nadal is into yet another French Open final. The world No. 12 won a set off the Spaniard, marking the end of Nadal's 37-set win streak in Paris.
Expect Nadal to disrupt the serve of the budding "Prince of Clay" while holding firm with his own.
Schwartzman had the first advantage but dropped on a forehand shot.
There have, however, appeared to be one or two chinks in Nadal's armour at Roland Garros this year. He has won every final he has reached, and in those 11 finals he has dropped just six sets.
And despite a late stutter as Schwartzman saved three match points, Nadal wrapped up victory to keep alive his hopes of equalling Margaret Court's record of winning a single Grand Slam singles title 11 times. It's the first semifinal between a pair of American women at Roland Garros since Serena Williams beat Jennifer Capriati on her way to the 2002 title.
Top seed Simona Halep, twice a runner-up, takes on two-time major victor Angelique Kerber.
The first set had taken 57 minutes, in stiflingly humid conditions, but there was to be no let-up for the underdog in the second.
Cecchinato said: "It was a special tournament for me".
"If I want to beat him, I have to play that way like I did in Rome and in Madrid".
"I know I have to play my best, I have to improve a little bit".
Both players also held their nerve early on during the semi-final stage.
It is the second straight all-American girls' final at Roland Garros, after Whitney Osuigwe beat Claire Liu a year ago.
He has lost just twice in 87 singles matches at the French Open.
But it took Muguruza quite a while to get going against Halep, who managed to keep sending ball after ball back over the net.
The former world number one has canceled from the ATP 250 of 's-Hertogenbosch, scheduled next week on grass. It will be familiar territory for Thiem, though, who is playing in his third straight semifinal here and will be confident of reaching his first major final anywhere. By comparison, Nadal has won 16 majors. I love what I am doing. (Smiling). I made too many questions to myself.
The win continues Nadal's undefeated run on championship weekend in Roland Garros - the Spaniard has never lost in Paris after reaching the semifinals.
"I don't have any obligation to win, first thing".
Nadal will face Juan Martin del Potro in the semi-finals.
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