The underdog shocked Djokovic on Tuesday, beating the 2016 Roland Garros champion 6-3, 7-6, 1-6, 7-6.
"To be able to win that first set and get ahead was crucial".
"Me and my brother (Mischa) are guys that spend three, four hours a day in the gym, lifting heavy weights, on the treadmill. It paid off today".
Djokovic had two set points at 6-5 in the second but went on to lose the tiebreak.
Thiem, the only man to beat Rafael Nadal on clay this year, held off a short-lived Nishikori revival on Court Philippe Chatrier to set up the meeting with Zverev.
His only previous run to the last 16 at a major was at Wimbledon a year ago and he next play either French 15th seed Lucas Pouille or Russia's Karen Khachanov.
"I hope we have many more matches at the Grand Slams but when we are 100 percent".
"He's an awesome player". I don't know if I'm going to play on grass.
Serbia's Novak Djokovic celebrates winning his fourth round match against Spain's Fernando Verdasco. Since then, employing a smooth one-handed backhand, he has beaten players seeded No. 8 (David Goffin) and No. 10 (Pablo Carreno Busta), before adding former No. 1 Djokovic to his list.
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Seventh seed Dominic Thiem muscled his way into the fourth round of the French Open, putting out Italian claycourt specialist Marco Berrettini 6-3 6-7 (5) 6-3 6-2 to set up a tie with Nishikori.
"For me, it's the first time semi-final grand slam".
US Open champion Stephens brushed aside Russian Daria Kasatkina to set up a repeat of last year's Flushing Meadows final with fellow American and good friend Keys.
"It was the best moment of my life", Cecchinato said.
Playing at his lowest ranking for nearly 12 years after months of struggling with an elbow injury and indifferent form, Djokovic has made the last eight by dropping just one set.
While defeat will be painful Djokovic, who has spent 223 weeks as world number one during his career, he will reflect on a positive claycourt season having reached the final in Rome and enjoyed a strong run in Paris before falling short.
The 31-year-old Serb said he did not "want to talk about tennis right now".
"Then once you get to the second week, every match obviously has more nerves, and there's more on the line".
By the end, though, points were tight and taught, one even lasting 30 strokes.
An elbow injury has limited the 12-time Grand Slam champion's playing time this year, while he was treated on his neck during the defeat by Cecchinato.