
World number one Novak Djokovic plays Alexander Zverev on Friday with the victor to play Thiem in the other semi-final.
The other singles match played today saw Russian Daniil Medvedev defeat Argentina's Diego Schwartzman 6-3, 6-3 to remain the only undefeated player at London's O2 Arena.
Tsitsipas, 22, felt disappointed with the third set.
World number three Thiem was the better player in the first set, sealing it with an ace after breaking serve at 5-5.
Last month Nadal hoisted his 13th French Open title to equal Roger Federer's record of 20 Grand Slam crowns.
A fired-up Rafael Nadal then fought back into the set after he got the break back with a stunning forehand passing victor at 3-4.
Medvedev, 24, immediately found his focus at the start of the second set, winning his first service game to love before Nadal double-faulted to give the Russian a 2-0 lead.
Thiem's record against Djokovic now stands at 5-7, against Nadal it is 6-9, while he leads Federer 5-2.
"I, for sure, can cause him some trouble", Medvedev said.
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Medvedev hasn't played Nadal since that London loss last November and says the rematch is a new opportunity.
In the second set against Djokovic, Thiem's ace put him ahead 6-5 in the tiebreaker, one point from victory.
Regardless of what happens at the weekend, when the semi-finals and Final will take place, it is possible to argue that the general standard of the play at the tour-ending event this time around has been the highest that it has ever been in London, and arguably the highest it has ever been since the first edition of the tournament in Tokyo in 1970. "It is a great pleasure to play against all of them and I am really looking forward to tomorrow". "I wasn't playing in the moment".
Medvedev looked the more likely victor as he raced through his service games in the opening set while Nadal laboured.
"I wanted to win the match, 100 per cent, but the first two matches were pretty tough, pretty long".
The 23-year-old fifth seed saved two break points on his serve in the following game, letting out a roar as he kept his nose in front.
The fact that he managed to shrug off the disappointment of double-faulting on one of his match points, then finish the match with a blaze of brilliance to stun Djokovic, speaks volumes for how far he has come.
Thiem will try to complete a breakthrough year, in which he claimed his first Grand Slam title by winning the U.S. Open, against either Rafa Nadal or Daniil Medvedev in Sunday's climax, guaranteeing a first-time champion for the fifth year in a row.
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