But as the Spaniard struggled to win points on his first serve, he was broken again for 5-4 and Schwartzman served for the set.
While Nadal's dominance in Paris can never be doubted, this year's inexorable march to the final has illustrated the paucity of genuine challengers, especially in the absence of Andy Murray and Roger Federer, and with Novak Djokovic being some way from his best after injury. It will be followed by the all-American matchup between Madison Keys and Sloane Stephens.
Increasingly frustrated at Cecchinato's resistance, Thiem lost his composure completely in the second set.
The second set turned into a tight tactical battle with neither able to break serve.
Schwartzman compiled a 20-4 edge in winners for the set, closing it with a forehand that landed right at the baseline.
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"It is nearly impossible to beat Rafa", said Del Potro who had his chances but failed to convert any of his seven break points before his challenge petered out into tired hopelessness.
The world number one has won all five of his meetings with 11th seed Schwartzman. The Austrian has already won two titles (Lyon and Buenos Aires) this season and had also reached the final of Madrid Open last month.
Nadal raised his level when it mattered much and fended off three break points in the eighth game.
Thiem has certainly been the second-best player on clay over the last two seasons.
Unseeded Japanese pair Eri Hozumi and Makoto Ninomiya will take on sixth-seeded Czech duo Barbora Krejcikova and Katerina Siniakova in the French Open women's doubles final.
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In order to get a shot to defeat Nadal on clay, Thiem had to first get past an improbable semifinalist, No. 72 Marco Cecchinato, which no one else had managed to do at this edition of Roland Garros.
Nadal wins his 11th French Open title.
If Thiem wins on Sunday, he will be the youngest man to win at Roland Garros since Nadal won at 24 in 2010.
Thiem grabbed a 2-0 head start in the first set as his powerful serve was fully charged and his approach to the net ruthless against a nervy Cecchinato. "I was very scared but that's sport".
"Yeah, if I won the second set, I think is totally different the third set", he said.
"For me, the motivation to play here always is high, high as possible".
Nadal crushed del Potro's spirit with the intensity of his tennis in the second set, bounding 5-0 ahead before the Argentine registered a game to lift the spirits of his fans.
Top-ranked Simona Halep will have another shot in the French Open final.
The 21-year-old Nadal became the first man since Bjorn Borg in 1980 to win three successive titles at Roland Garros.
Also back in action after a suspension was the quarterfinal between past U.S. Open champions Marin Cilic and Juan Martin del Potro. "I have gone a very long way now and I don't want to lose the finals; otherwise, it's not a very nice feeling".
They were at 5-all in a first-set tiebreaker when their match was stopped. It was part of a run in which he claimed 14 of the last 17 games to overwhelm the No. 5-seeded del Potro 6-4, 6-1, 6-2 and earn yet another spot in the title match at Court Philippe Chatrier.