Earlier Thiem needed to survive a nasty bout of the jitters to see off Marco Cecchinato and reach his first grand slam final.
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The 10-time champion served out the match to complete his victory in two hours and 14 minutes and set up his date with Thiem, the pretender to his throne.
"It was a very hard first set and Juan Martin had lots of opportunities".
Nadal, by contrast, had not had a sniff on Del Potro's serve until, at 5-4, two swishes of his forehand forced two set points, the second of which he converted when the Argentinian netted.
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"I know I have to play my best, I have to improve a little bit".
At least Thiem can boast being the only man to have defeated Nadal on clay in the last two years.
Croatian Cilic played an terrible game when serving for the set, making four unforced errors, but he was gifted another chance to serve for the set after breaking Del Potro again and at the second time of asking he levelled the match.
"Thiem is an awesome player". That said, Nadal is on clay and picking against him to lose on this surface at the French Open seems like a foolish move.
"I believe that there is chances, limited chances in your career", Nadal said. "That's why he's the No 1 and beating all the guys", said Del Potro. 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.
Juan Martin del Potro took his frustration out on a fan during his quarterfinal Roland Garros encounter with Marin Cilic-though he couldn't quite figure out which spectator to zone in on. I had a lot of break points.
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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. "But I wasn't focused in that moment, so I made the mistake". "Of course, the rain helped stop the match and helped me think about the match, and that's a reality. He deserved to win".
After del Potro served out his victory at love to get to his first semi-final at the clay-court Grand Slam tournament since 2009, he sat in his changeover seat, chest heaving.
Cecchinato had sent Novak Djokovic packing in a thrilling quarter-final but Thiem's class on clay proved too much.
"I need to regenerate and have a good breakfast to keep up my good level".
Day 13 at the French Open action is men's singles semi-finals day, and with three big names and one rather unlikely contender taking to the courts, Dan Weston previews the matches.
"He likes the conditions more here than in Madrid, for sure", said Thiem, who lost in straight sets to Nadal here in the 2017 semifinals.
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"Not a very nice feeling", Thiem said.