He later described the win as "one of the best matches I have played on clay".
Djokovic will continue working with long-time former coach Marian Vajda until the end of the claycourt season after linking up with the Slovak again for the first time in nearly a year in Monaco.
More of the same was expected in the second set with how strong Nadal was plus the fact that Thiem could not get anything going.
Now, the 31-year old will meet Bulgarian fourth seed Grigor Dimitrov in the last four for a berth in the finals.
Dimitrov booked his place with the first straight-sets win of his tournament, on the other hand, beating Belgium's David Goffin 6-4, 7-6 (5) to set up a meeting with Nadal in the last four. I always said that. "Hopefully in my next match I can do better in those moments".
Dimitrov and Goffin were playing for the first time since the Belgian suffered a freak eye injury during their match in Rotterdam earlier this year.
Nadal subsequently served out a set in which he 13 winners to the three from the racquet of Khachanov, who committed 12 unforced errors in the opener. Given that this was a clash between 2 of the best clay court players, Nadal would have to dig deep.
The Spanish veteran is challenging for a record 31st Masters title, 24 of which have been on clay. "I don't see myself missing Monte Carlo on goal".
Having previously captured titles in Monte-Carlo, Barcelona, and Madrid, Nadal was clearly tired in his Rome setback, but there will be no such issues this time around. "He asked me about things". I can't let him play in comfortable positions because then it will be impossible. I tell him the things that I think worked for me.
"Comebacks are not easy", Nadal added.
"I know how tough and frustrating is when you work every day and you don't see the light of how to improve". Nadal said."That's what I really hope about [Murray] because he is important, very important, for our Tour".
"If Andy is healthy, he will come back". A backhand cross-court found the sideline, leaving Thiem with little chance to get it over and giving the 10-time champion in the principality, the lead.
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