Thiem should provide sterner resistance in the last eight, but in this form it is hard to envisage anybody stopping Nadal extending his own record to 11 Monte Carlo titles.
The 12-time Grand Slam champion, playing only his fourth tournament since Wimbledon last July after struggling with a right elbow injury, overcame some late nerves to win 7-6 (7/2), 7-5. But Thiem is one of a rare band of men who has claimed victories over the mighty clay champion: in 2016 in Buenos Aires, and past year in Rome-which was the only clay tournament of the five Nadal played that the Spaniard failed to win.
Next for Thiem is World No. 1 and King of Clay Rafael Nadal who blew out Karen Khachanov 6-3, 6-2. He took it when Struff hit a powerful forehand narrowly wide, and let out a yell of relief.
Nadal will no doubt enter the tie as the favourite but it may well prove to be the match of the tournament, and it certainly stands to reason that it will be the 31-year-old's toughest match of the week.
Djokovic, in contrast, crashed out in a gruelling three-set match to fifth seed Thiem, losing 7-6 (7-2), 2-6, 3-6 to the Austrian, in a clash that lasted two hours, 29 minutes.
Djokovic has won the title twice, including when he ended Nadal's 46-match winning streak by winning the 2013 title.
"It's way better feeling if you go contrary to him (Nadal) and be aware you've conquered him on the particular surface", the 24-year-old Thiem explained. I played without pain in the elbow, which is important.
But while most of his finals have come on hard courts, he is often cited as a clay expert courtesy of early breakout runs on the red stuff, and he picked up some big scalps in Monte-Carlo a year ago: Dominic Thiem and Novak Djokovic, before falling to Nadal in the semis.
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While there were some promising signs for Djokovic early on as he fought back from a break down to take the first set, Thiem was able to take control of the contest midway through the second set.
Bulgaria's Gregor Dimitrov and Germany's Alexander Zverev also won the match.
Djokovic will next face Borna Coric of Croatia, who beat French veteran Julien Benneteau 6-2, 6-3.
Also on Thursday, Frenchman Richard Gasquet claimed his 500th career victory in defeating German Mischa Zverev 6-2, 7-5.
Novak Djokovic, who recently parted ways with Andre Agassi, was defeated by Dominic Thiem in three sets at the Monte Carlo Open earlier today.
Second-seeded Marin Cilic advanced without hitting a ball after Milos Raonic pulled out with a right knee injury.