Thiem won 7-5, 7-6 (12-10), 6-1 victory to earn a place in a Grand Slam final for the first time, while Nadal crushed Argentine fifth seed del Potro 6-4, 6-1, 6-2 to enter the French Open final for the 11th time.
The Spaniard is just the second man in the Open Era to advance to 11 championship matches at a single Grand Slam, joining Roger Federer, who has won eight titles from 11 finals at Wimbledon.
The second set tie-break proved to be decisive as the Italian Cecchinato squandered three set points, having recovered from a 6-3 deficit, reports Efe.
Cecchinato, who up until this year's Roland Garros never got past the first round of a Grand Slam event, did not look the same in the third set, as he hit just one winner, committing eight unforced errors.
This was not the case during the first two tight sets between the Thiem and Cecchinato.
Thiem, who fell short to Spaniard Rafael Nadal at the semi-finals in 2017, started the match breaking his rival Cecchinato's serve.
The 25-year-old Cecchinato, who knocked out Serbia's Novak Djokovic in the previous round, however, fought back, drawing level at 4-4, but eventually conceded his serve in the 11th game.
Thiem improved on serve during the second set, facing zero break points, but he was not able to seize on any of the three break points as the set went to the tie-break.
"The second set tie-break was the big key to the match, 100 percent because obviously, he felt all the matches from the past two weeks after that," said Thiem, according to ATP's website.
"If he would have won the tie-break, he would (have been) full power, for sure, in the third set. So it was good for me that I won it ... I expect that he will be a really good player on clay. You don't get to a Grand Slam semi-final by accident. He beat really good players."
Easing through the third set, Thiem became only the second Austrian player to reach the final of Ronald Garros, following in the footsteps of Thomas Muster, who won the title in 1995.
"Of course there is pressure, especially in Grand Slam finals, because I have gone a very long way now and I don't want to lose the final," said Thiem.
Cecchinato said: "It was a special tournament for me. I played two sets at the same level (as Djokovic) against Thiem. (My) level is very good at the moment (and) I am very happy. If I had won the second set, I think it would have been totally different. But after the loss, I go a little bit down mentally and physically."