Nadal appeared to have salvaged the opening set when he broke Thiem back for 5-5, but the Austrian took the advantage right back after Nadal sent a forehand into the net.
Thiem unsettled Nadal from the start, breaking his serve twice in the first set.
Thiem then struck an ace to complete the set.
Nadal, somewhat sassily, pointed that out to the Austrian after his 7-5 6-3 victory - warning him that he has a long way to go to be considered as one of his toughest rivals on clay.
Nadal is 6-2 in his career against Thiem, with every one of those matches coming on clay, but as Thiem alluded to, the biggest tests for the Spaniard in this head-to-head matchup have certainly come in Madrid and Rome.
Early in the second set, Nadal was in trouble again. Even so, Thiem struggled to take charge, turning the set into a topsy-turvy affair. Nadal hit the ball at his feet, but Thiem managed a half-volley that turned into an irretrievable drop shot. Up 40-15, the world number one's groundstrokes were errant.
Thiem's first set win came with the highlight of the match - a thrilling back-and-forth point that pushed both players up, down, and sliding all across the court.
In the second, Thiem continued to hammer away at Rafa, but couldn't hold a 3-1 lead.
"I had to play an extraordinary match, and that's what I did", said Thiem. But Nadal served his way out of trouble.
Next up for Lajovic will be South African world No. 8 Kevin Anderson, who defeated German Philipp Kohlschreiber 6-3, 7-6 (9-7) in the third round.
Meanwhile, Halep was broken four times by Pliskova as she missed out on a place in the semi-final.
Despite being off-key against Thiem, he said he was now fully fit as Paris looms. This is unbelievable. So, I had to play an extraordinary match, and that's what I did. That was not the case today. "Let's not talk about that anymore and let's continue on what we have ahead which is what I am concerned about", Nadal said. "That's the end of the story". While the win was an upset, Thiem is no pushover - ranked No. 7 in the world and with his best tennis also coming on clay.
Nadal will now focus on next week's tournament in Rome where, should he win the title, he could reclaim the number one ranking from great rival Roger Federer who has opted to sit out the claycourt season in preparation for Wimbledon and beyond.
"Being honest, I am not - as I said a lot of times - when I am winning, I am not super happy, and when I'm losing, I'm not super sad".
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