Nadal booked his place in the quarter-finals of the second major of the season after registering a comfortable 6-1, 6-2, 6-2 win over Roberto Bautista Agut of Spain.
The amount of power Thiem possesses has allowed him to comfortably hold serve, and that is something he will have to continue with against Djokovic at all costs.
Thiem had just beaten Rafael Nadal a day earlier in Rome.
The fourth-seeded Nadal marched into the quarterfinals for the 11th time with another commanding clay-court performance in Paris.
Danish 11th seed Caroline Wozniacki knocked off 2009 champion Svetlana Kuznetsova of Russian Federation 6-1, 4-6, 6-2 to reach the last eight for just the second time.
Pliskova, the Czech, beat Carina Witthoft of Germany 7-5 6-1, while Svitolina of Ukraine overcame Poland's Magda Linette 6-4 7-5.
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The win was Carreno Busta's first over a top-10 player. When a player admits to something like that, it's rarely if ever a good sign for their next battle.
"I still can't believe that I'm sitting here".
He wasted three of them serving at 5-4 up, and three more when serving at 7-6.
Novak Djokovic and other players at the French Open say they are not anxious about competing at Wimbledon next month despite the recent attacks in Britain. They have played just once before, in the second round of Rabat in 2015. She just came out with great tennis a lot of the time.
Since arriving in Paris, Muguruza has been looking to reprise the punishing baseline hitting that carried her to this title past year, but yesterday she kept on botching the final put-away.
"I hope things are going well for him, and he's someone I really like".
Williams, whose sister Serena is not playing in the tournament as she is expecting her first child, ran out of steam in the last two sets. He had to get to seven games in each of the first two sets against fan favorite Gael Monfils but he moved on in straight sets.
"Everything wasn't flawless. There were a few concerns", Mladenovic said, before joking: "I made about 35 double-faults today, but everything's OK!"
"I then threw some cold water on my face and told myself not to finish the Sunday like that". Against Rafa, I played with the last percents I had.
Defending champion Garbine Muguruza and French favorite Kristina Mladenovic are heading to a third set at Court Suzanne Lenglen with a Roland Garros quarterfinal spot at stake.