"It's the best, a five-set match".
Nishikori took his only break point opportunity to claim the third set but Thiem, twice Roland Garros semi-finalist, regained control in the fourth.
Nishikori seized his first break opportunity at 6-5 to take the set when Thiem's forehand flew long.
Play was suspended due to fading light, with Russian Daria Kasatkina leading 7-6 (5) 3-3 against second-seeded Caroline Wozniacki.
The 2016 champion Novak Djokovic was beaten 6-3, 7-6 (4), 1-6, 7-6 (11) by Italian Marco Cecchinato in a late quarter-final match, after a battle that lasted almost 3 ½ hours, which produced several scintillating rallies. Nadal and Federer have returned from injury and surgery respectively to dominate the scene since early previous year, topping the ranks, winning the last five Majors between them, with Nadal favourite to win his 11th French Open this week.
Thiem was knocked out by Djokovic in the last four in 2016 before losing to Rafael Nadal at the same stage a year ago. "I'm not that young anymore", said Thiem.
He then needed four sets to overcome the talented Greek teenager Stefanos Tsitsipas and also dropped a set against Italy's Matteo Berrettini, winning 6-3 6-7 6-2 6-3. The German has won 34 tour-level matches this season, more than any other player in 2018 and one more than his nearest rival Thiem. Meanwhile, Serena Williams and Venus Williams were bagelled in the deciding set as they were dumped out of the women's doubles at the French Open yesterday by third seeds Andreja Klepac and Maria Jose Martinez Sanchez.
Broadcaster ITV has all the coverage of the French Open this year, covering the Grand Slam from 9.30am-9pm every day until the latter stages.
Stephens next faces Keys in a rematch from the US Open final.
The 23-year-old will next face U.S. Open runner-up Madison Keys.
The Austrian was beaten by eventual champions Novak Djokovic and Rafael Nadal in his last two appearances in the last-four but will hope to go at least one step further this time around, with a meeting with the Serb once again on the cards.
"Coming on to play on back-to-back days in a Grand Slam, I was really pleased to get out there and play some good tennis", American Stephens said. That left the Austrian facing a hard challenge in Nishikori, but Thiem made fairly light work of it to again win in four sets, 6-2 6-0 5-7 6-4.
He cruised through the first set, held his nerve in the second set tiebreak, survived a comeback from former world number one Djokovic in the third, before prevailing in a highly-entertaining fourth-set tiebreak.
"At the end I was nervous". "So hopefully next time I will win it..."
Having said this, Thiem's statistical edge is paper-thin and certainly not enough to justify a lower market price, so it is utterly evident that the market is factoring in a lack of faith in Zverev's ability to back up three consecutive 3-2 victories and in short, thinking that the German will be absolutely knackered from a fitness perspective.