The 21-year-old world number three had battled through three consecutive five-setters on his way to the last eight, but his body failed him against claycourt specialist Thiem.
He and Zverev were certainly locked in a promising rivalry thus far.
For the second straight year, he is the only man to have defeated Nadal on clay prior to the French Open. But of the last three matches, the 6ft6in German had won two, the last in the Madrid final last month.
I hope this is not the end here. What neither lacked was fight.
Visit the Roland Garros website for the results in full. While Zverev batted away questions about whether a third five-set match would start to take its toll, there is no doubt that Thiem in a best-of-five is not going to be easy - he should expect either four or five sets for sure.
Nearly 12 hours altogether so far.
Zverev began to let rip, snatching one game back, but the outcome was inevitable and Thiem put him out of his misery with a routine backhand victor into a wide-open court.
But the greater power of Keys paid dividends in the breaker, as the American finally took the opener on her fourth set point with her 18th victor.
In a meeting between the two youngest players remaining in the men's singles it was the 22-year-old Khachanov who secured a decisive second break to win the first set.
Djokovic, seeded 20 after a year of struggles with an elbow injury and mediocre form, was never in trouble against an erratic Verdasco, who needed treatment for a badly blistered left foot at the end of the second set. The Austrian offered up a break-back point with a double fault, but compensated with remarkable reactions at the net, threw in another drop/lob combo, and led 3-1.
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The conclusion came swiftly, with Zverev increasingly unable to respond in rallies. He was again taken the distance by Damir Dzumhur in the third round, saving a match point along the way. "So I think we can make it legendary and that would be very nice", Thiem, 24, said. Both are in the quarterfinals in Paris for the first time.
"I have practiced with him many times in Monte-Carlo when he was part of the Ricardo Piatti Academy team, and he trained a lot where I live".
"I think for me it's time to move on to make a great step, because I'm turning 25", he said. Rafa Nadal goes in search of his 11th French Open title but don't count out Novak Djokovic - and what about the in-form Alexander Zverev?
In a tight first set of a match played in overcast, heavy conditions, Thiem converted the only break point off a backhand victor in the seventh game before securing the opener with an ace.
"At the Grand Slams, there are the big four".
"I don't know if I'm going to play on grass", Djokovic, who won the last of his 12 Grand Slam titles in Paris two years ago, told reporters crowded into a small interview room after he declined the opportunity to use a much larger one.
"I'm young, so I might as well stay on court and practise a little bit", said Zverev.
"I thought I played pretty solid", Stephens said.