After a tight first set which Thiem took after prevailing 7-5 in the tiebreak, the Austrian cruised to his first win in six meetings with the 12-time major victor.
Thiem was beaten by Djokovic in his only other run to the last four of a grand slam past year and was hammered by him in Rome last month, but gained revenge with a 7-6 (7-5) 6-3 6-0 victory on Court Suzanne Lenglen 12 months later.
The defending champion fell to the man he beat in the semi-finals in 2016, and will not participate in the last-four of a Grand Slam for just the second time in his career.
The fourth-seeded Nadal, a nine-time champion at Roland Garros, was leading 6-2, 2-0 when Carreno Busta stopped.
Yet to drop a set this year, Nadal will next face either Djokovic or Dominic Thiem in what is touted as the "real final", even though Stan Wawrinka, Andy Murray, Marin Cilic and Kei Nishikori remain in the top half of the draw. Just a pretty bad set.More news: Merkel says expects Britain to remain a partner post-Brexit
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"Trust me, I'm thinking about many things, especially in the last couple months", he said.
The last British player to win the men's singles French Open title was Fred Perry in 1935.
"I don't know how many games I lost this year, but I really don't care about this".
"I know that I have achieved the biggest heights in this sport, and that memory and that experience gives me enough reason to believe that I can do it again, although I'm aware that I'm not the only one", he said. So I guess you've got to go through it, learn your lessons and figure out the way.
It was Thiem's first win over the Serb in six meetings. Djokovic entered the day having won all five previous matches - and 11 of 12 sets - against Thiem, including in the French Open semifinals a year ago.
"It's fantastic for me", Thiem said.
Djokovic was asked during his post-match news conference whether he would prefer to take a break from tennis, rather than play through his issues.
Wawrinka's lone worrying moment resulted when he nearly turned an ankle near the net in the last game against Cilic.