Del Potro said resuming a match at 5-5 in a tiebreak with his serve to come had been a unusual situation but his aim was true and he moved 6-5 ahead before his cagey backhand slice induced a poor forehand error by Cilic.
This was the No 5-seeded del Potro's first semifinal at Roland Garros since 2009. Cilic is serving at love-30 in the 11th game.
Thiem's ability to bully opponents from the baseline was on display in his 6-4, 6-2, 6-1 victory over No. 2 seed Alexander Zverev in the quarterfinals.
The Argentine has never beaten Nadal on clay.
A few hours earlier, as Nadal and Thiem warmed up, the booming voice of the announcer at Court Philippe Chatrier detailed the bona fides of both. When play resumed on Thursday, however, Nadal returned to his dominance at Roland-Garros.
But at 4-5 Thiem's serve let him down badly, handing Nadal three set points.
The 37-set run was Nadal's longest at the French Open.
"Even if it was 6-3 6-4, it was an uncomfortable match for me".
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.
Up in the stands, Nadal's uncle Toni, his former coach, was nervous, too, "because I thought maybe we can have a problem", he said.
"I know how to play against him", he said, without elaborating.
"But all my semi-finals in Grand Slams were against them".
One of those victories came against Thiem in last year's semi-final and was, if anything, more comprehensive than this one. But she fell apart and eventually lost to the unseeded Latvian in her second French Open final.
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 German left-hander had lost in the first round in the last two years.
When del Potro avoided a bagel in the sixth game of the second, he raised his arms in celebration.
Otherwise, he stayed steady in a 7-6 (5), 5-7, 6-3, 7-5 win over No. 3 Marin Cilic in a matchup between two past U.S. Open champions. It was a first Grand Slam final for Thiem, a 24-year-old Austrian.
The No. 1-ranked Nadal compiled a 35-20 edge in winners while making only 19 unforced errors Friday. The Austrian won just one of the first nine points as Nadal immediately broke for 2-0.
"Today I played more aggressive".
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.
Nadal can become just the second male player in the Open era to reach 11 finals at the same Grand Slam tournament, equaling Roger Federer's record at Wimbledon.
Rafa will now face the victor between Marin Cilic and Juan Martin del Potro. hen he will either face Marco Cecchinato or Dominic Thiem in the final.
Romania's Simona Halep will first play American Sloane Stephens in the women's singles final tomorrow.