Standing in Murray's way is the man he beat in last year's semifinal, Wawrinka.
Thiem has beaten Nadal, Djokovic and Murray on clay already this year, while Kyrgios thumped Djokovic in back-to-back matches in Acapulco and Indian Wells.
Bethanie Mattek-Sands of the US and Lucie Safarova of the Czech Republic are one victory away from their second French Open women's doubles title and fifth major championship overall.
Thiem went into the match fresh from his stunning upset of defending champion Novak Djokovic and looking for a second successive win against Nadal.
The fourth set was even as can be - neither held a break point - but Wawrinka stepped up in that tiebreaker by winning its final three points, the last with a run-around forehand return victor delivered from wide of the doubles alley.
The Scot won five of the last six games to take the set, and looked favourite to claim the fourth with Wawrinka showing his frustration.
Top-ranked Andy Murray has won the third set against Stan Wawrinka 7-5 to take the lead in the French Open semifinals.
Rafael Nadal is now leading Dominic Thiem 6-3, 6-4 in their French Open semifinal. "I think that Rafael did not play at his best, but well enough".
Murray got within four points of victory in the fourth set but a misjudged dropshot helped Wawrinka grab the tiebreak and at the same time break Murray's resistance.
There were 4 breaks in 7 games.
Murray, who like Wawrinka owns three grand slam titles, made only one unforced error in the first seven games.
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The Scots have won only one of their last 10 meetings - and lost the return fixture 3-0 at Wembley in November. He is getting fitter all the time and he knows age is only a number. "He is looking the best I have seen him".
Zverev, who has joined Thiem in the top-10 this month, has failed to get beyond the third round of a Slam - although he is the youngest of the trio and did take Nadal to five at the Australian Open at the start of this year.
Two years ago when he won the title at Roland Garros, Stan Wawrinka made headlines not only for his tennis, but also for his pink-checkered shorts.
The same symbols are also displayed on the inside frame of his racket. And Murray capped his three-point run to claim the tiebreaker when Wawrinka put a forehand return into the net on a second serve at a mere 84 miles per hour (136 kph).
Murray won the first set 7-6 (6).
The quarterfinal match between fifth-seeded Elena Svitolina and No. 3 Simona Halep at the French Open is going into a third set.
His only win against one of his biggest rivals at a slam since beating Novak Djokovic in the 2013 Wimbledon final came in Paris past year when he edged out Wawrinka in the semis. He capped it, appropriately, with a backhand down the line, his 87th victor of the day, 51 more than Murray accumulated.
Murray dropped serve in the eighth game, but he broke right back. At the same time, Murray had nine winners as opposed to Wawrinka's 22.
Paris: World number one Andy Murray and fourteen-time Grand Slam champion Rafael Nadal will aim to book their place in the finals of the French Open when they take on their respective opponents in their men's singles last-four clash here today.
Wawrinka has proved tough opposition to some of the world's best, including Murray who struggled in his victories over the Swiss in previous meetings, and with neither of the Semi-finalists having dropped sets so far apart from Murray, it's certain that if the number one is to win on French soil where he has often struggled on their clay courts in the past, he'll have to dig deep. It was a triumph of offense over defense, as Wawrinka used his sublime one-handed backhand and hammer of a forehand to send Murray scrambling and sliding all over the red clay at Court Philippe Chatrier for a tad more than 4½ hours of compelling action.
Unusually for Wawrinka at a grand slam, he entered the semifinal in nearly flawless form, not dropping a set.
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