Second-seeded Alexander Zverev has reached his first Grand Slam quarter-final the hard way, beating Karen Khachanov 4-6, 7-6 (4), 2,6, 6-3, 6-3 on Sunday for his third straight comeback win in five sets.
Thiem beat No. 19 Kei Nishikori of Japan 6-2, 6-0, 5-7, 6-4 on Court Philippe Chatrier.
He hit 73 unforced errors, dropped serve eight times and served up seven double faults.
When Jonathan tried to turn the subject back to sport, telling the rising star "you clearly love your tennis", Zverev responded 'not as much as your accent!'
"It was an wonderful, high level match", said Zverev.
"Hopefully many more to come, " he said in his post-match on-court interview.
But Zverev edged a tense fourth set in which he was issued a code violation for being coached from the stands by his father Alexander Sr.
Keys next faces unseeded Yulia Putintseva of Kazakhstan, who beat 26th-seeded Czech Barbora Strycova 6-4, 6-3. An ace gave him another set point but he missed that one, too, putting a low volley into the net.
Djokovic has now made the last 16 of a Slam for the 43rd time, tying Jimmy Connors on the all-time list, second only to Roger Federer´s tally of 60.
The match didn't end well for the Bosnian either.
Serbia's Novak Djokovic with Spain's Fernando Verdasco after winning their fourth round match.
Bautista Agut was playing in Paris despite the death of his mother last week. "It's the best, a five-set match".
Thiem, a semi-finalist at Roland Garros for the past two years, has won eight of his 10 ATP titles on clay and dominated on his favoured surface.
"You have to draw the line and, you know, look for the next chapter", said the world number five.
Stephens next plays either Australian Open champion Caroline Wozniacki - seeded second - or 14th-seeded Russian Daria Kasatkina.
He's also somehow only made the fourth round once before, at Wimbledon past year.
US Open runner-up Madison Keys saw off Japanese 21st seed Naomi Osaka 6-1, 7-6 (9/7), setting up a last-16 tie with 31st seed Mihaela Buzarnescu.
Still, Keys served for the victory at 5-4, and held a match point at 40-30, when she pushed a backhand long and wound up getting broken.