It's the best, a five-set match.
Zverev was coming off a trio of wins that went five sets and, while still just 21, could not will his body to another comeback.
Play was suspended due to fading light, with Russian Daria Kasatkina leading 7-6 (5) 3-3 against second-seeded Caroline Wozniacki.
Keys, the US Open runner-up to Stephens past year, will face Kazakhstan's Yulia Putintseva for a place in the semi-finals, after the world number 98 saw off Barbora Strycova 6-4, 6-3.
Stephens next faces Keys in a rematch from the US Open final.
"I didn't win it today, but it's a positive sign", said Khachanov. "It will be a pleasure to play against Novak".
Yes, Djokovic was thrilled to get back to a ninth consecutive quarterfinal in Paris after dealing with elbow trouble for more than a year and needing surgery in February.
It was the Serb's 200th Tour-level clay court match win.
For the former champion, though, it was not to be as he came up against the unseeded Marco Cecchinato in blistering form, and lost a gruelling and highly intense four-setter, 6-3, 7-6 (4), 1-6, 7-6 (11). Wozniacki did however make the quarterfinals previous year in Paris prior to losing to the eventual champion Jelena Ostapenko.
Kazakh Yulia Putintseva produced a clinical display to beat 26th seeded Czech Barbora Strycova 6-4 6-3 in exactly one hour and 30 minutes.More news: Ovechkin and Capitals overcome final hurdle to win Stanley Cup
Both Zverev and Thiem, who were dubbed as two of main threats for Nadal at Roland Garros 2018, have been making heads turn with their performances on clay-court over the last few seasons.
Thiem will be looking for revenge as he was handed a straight-game thrashing the last time the two youngsters met - Madrid Open final in May.
Paris - Dominic Thiem reached his third successive French Open semi-final on Tuesday with a 6-4, 6-2, 6-1 demolition of a hobbled and exhausted Alexander Zverev who admitted he was close to quitting the tie. Nishikori rallied in the third game, which went to deuce five times before he was broken again and won just two points over the final three games.
I hope this is not the end here.
"It's something very special to serve for the French Open quarters", the Austrian player said after clinching his game-winning point.
The latest gritty victory came with the usual temper flare-ups from Zverev.
Unfortunately the match-up was ruined as a contest when Zverev, playing his first Grand Slam quarter-final, pulled his left hamstring midway through the second set.
Zverev also arrived at Roland Garros past year with high expectations after winning the Italian Open, only to slump to a first-round defeat by Fernando Verdasco, before further early exits at the US Open and the Australian Open in January. I was hurt a little bit. He moved through Tuesday's quarterfinals 6-4, 6-2, 6-1, reports Xinhua news agency. "All the hours in the gym have paid off".
"Firstly, I'm really excited to be in my first quarter-finals in Paris", Keys said.
Having escaped Saturday - 8-6 in the third set over Camila Giorgi - Stephens had a surprisingly simpler time in the fourth round, easing past 25th-seed Kontaveit 6-2 6-0.
Keys prevailed 6-1 6-Four and hasn't dropped a set on the floor she finds essentially the most hard.