Nadal was completely dismantled by Thiem in the first set as the American crowd was shocked into silence in NY, the Austrian hitting vaporising forehands and backhands to wrap up the opener in just 24 minutes - tallying 13 winners, five aces and 24 points in total compared to just seven from the former.
Nadal, a three-time U.S. Open champion, had lost to Thiem in the quarterfinals of the Madrid Open in May, but pummeled him in a lopsided French Open final in June.
"I'm very, very sorry", Nadal revealed he'd said to Thiem as they embraced.
Remarkably, Thiem was the first top-20 player Nadal has faced at Flushing Meadows since his final win over Novak Djokovic in 2013.
The semi-final will pit Nadal against third seed and 2009 US Open champion Juan Martin del Potro for the second successive Grand Slam tournament. That win should build confidence for Thiem as he takes on the tournament's number one ranked player.
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"I think that moment was the key of the match", Del Potro said in an on-court interview. The fifth set brought a great tennis as well, with Thiem saving two break points at 2-2 to remain on the positive side of the scoreboard.
"The match was special for its different phases", Nadal said afterwards.
With Nadal eager to finish off the match in straight sets in energy-sapping humidity, Basilashvili twice came from a mini-break down to take the set, leaving his opponent to rue a missed forehand down the line at 6-6. Not only was Nadal two points from losing at 5-all in the closing tiebreaker, but he finished with fewer total points, 171-166. "It's good to have now two days [without a match] that probably give me the chance to be 100 per cent in the semi-finals".
The young Austrian used savvy court positioning and one of the best performances of his life to earn a 7-5, 6-2, 7-6 (2) rout Sunday and his first trip to the U.S. Open quarterfinals.
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The German tactician said he expected the mistake but urged his players to stop putting their goalkeeper in hard situations. But he did it. "Then it's games, games, games and the whole of September - I don't know how many , but a lot".
Soon after that, Williams went from trailing 4-2 to not only taking the first set but also leading 4-0 in the second.
The Nadal who was gassed and wearing a cooling vest during breaks in the first set was no more.
It was the longest match of this year's US Open and Nadal jumped over the net to console 25-year-old Thiem after the victory.
The Austrian was heartbroken but proud, saying: "It's going to be stuck in my mind forever. He will have his chances in the future without a doubt", Nadal said. But Thiem closed out the game after giving up the first three points, putting Nadal under the gun, serving to survive to a tiebreak.
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