Nadal returned with his famed forehand finally firing on all cylinders, earning back-to-back breaks to move within a hold of the set.
He saved three set points in the second before winning an epic tiebreak, something which Cecchinato has become famous for this year at Roland Garros. Schwartzman saw two set points come and go but at the third time of asking, after a delay while a spectator was helped out after feeling ill, the Argentine ripped a forehand victor.
Caty McNally and Cori Gauff will meet in an all-American girls' final at the French Open after winning their semifinals.
Nadal said he was a "bit lucky" the match was halted by rain.
Breaking serve in the first game and bouncing to a 4-2 lead, Thiem controlled proceedings before Cecchinato reeled off the next three games with trademark flair and adventure.
But despite the straight-sets win, it wasn't a cakewalk for the Austrian.
"I am very happy to be back in the final here at Roland Garros". He then played an ATP 250 tournament in Lyon the very week before French Open, an often unheard practice from a top 10 player ahead of a Slam - and won it - just to keep the momentum going.
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That win, according to three-times former champion Mats Wilander, should be all Thiem is thinking about when he prepares for Sunday's clash.
He buckled at 5-5 though and sent a backhand long on break point, leaving Del Potro to serve for the match, which he did easily as Cilic sent three more backhands out. It puts them in an uncomfortable position since the start - they lose the first set and immediately think "oh, there's no way I can get three sets now, I'm not physically strong enough to do it". "I missed a lot at the beginning of the match".
"Life came at me fast after the U.S. Open", said Stephens, whose late father, John, was the 1988 NFL Offensive Rookie of the Year with the New England Patriots.
They have not played on clay for 11 years, however, so it will be a step into the unknown on Friday.
Nadal did not have almost as hard a time against the fifth-seeded del Potro. At No. 72, he is the lowest-ranked French Open semifinalist since 1999. And he did just that, easier opponent notwithstanding, with a 7-5, 7-6 (12/10), 6-1 win.
Nadal saved another three break points before holding with a sublime victor, then unleashed a couple of magnificent shots and Del Potro netted a backhand to lose a set which he had the better of.
Once Nadal stole the opener with a break in the 10th game it was one-way traffic as he left Del Potro trailing in a cloud of Parisian clay dust to set up a final against Dominic Thiem. Coincidentally, the only time he has looked in any danger was on day 11 when Diego Schwartzman, the 11th seed, took the only set of the tournament off him.
Schwartzman had a point to lead 4-2 but a forehand error allowed Nadal off the hook.
In the other remaining quarterfinal, also suspended on Wednesday, No. 3 Marin Cilic and No. 5 Juan Martin del Potro will resume at 5-all in a first-set tiebreaker.
One of those was a 6-3, 6-4, 6-0 rout in the Roland Garros semi-finals 12 months ago.