The 30-year-old Serb, who has prevailed in some of the sport's epic battles on the way to 12 major titles, was barely recognisable as he capitulated in a 7-6 (7-5) 6-3 6-0 defeat by Austria's Thiem in the quarter-finals.
Thiem is the only player to beat the history-chasing Spaniard on clay this year, in the Italian capital before losing to Djokovic, but knows he will need to produce something special to repeat that feat in Paris.
The world number two was uncharacteristically flat - particularly during a third-set bagel - as he was humbled in two hours and 17 minutes.
The Austrian sixth seed swept aside Horacio Zeballos 6-1 6-3 6-1 to book a last-eight clash with Novak Djokovic.
Nadal was leading 6-2, 2-0 when Carreno Busta retired after suffering abdominal injury.
As a result of the downpours, all four men's quarter-finals will be played on Wednesday with Andy Murray against Kei Nishikori and Stan Wawrinka facing Marin Cilic. "Just pretty bad set". It's only the second time Djokovic lost a final set by the score of 6-0 in his 937 career tour-level matches.
"The past few months, I have been playing very well", said Nadal.
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Roger Federer (13 Australians, 11 Wimbledons and 10 US), Jimmy Connors (14 US and 11 Wimbledons), Andre Agassi (10 US Opens) and Djokovic (10 US Opens) are the others. Thiem erased the first with a forehand volley and the other with a service victor that prompted Djokovic to roll his eyes.
In a match dubbed "the final before the final", Romanian Simona Halep plays Ukraine's Elina Svitolina.
Djokovic's backhand really let him down in the tiebreaker: All seven points won by Thiem ended with that stroke.
Murray is in the semifinals in Paris for the fourth year in a row. Nadal said. "I only care that I am in the semifinals".
The Scot set up a semi-final rematch with third seed Wawrinka after beating the Swiss in four sets at the same stage a year ago.
Wawrinka's lone worrying moment resulted when he nearly turned an ankle near the net in the last game against Cilic.