Nadal began his US Open campaign with a victory when his compatriot former world #3 David Ferrer was forced to retire in the second set, in what was his final Grand Slam appearance.
The finale also went to a tie-break and Nadal edged it to secure a 0-6 6-4 7-5 6-7 (4-7) 7-6 (7-5) win at 2.03am local time.
After suffering a first set "bagel", Nadal had to battle back from breaks in the third and fourth sets before seeing off the first top 20 player he had faced at the US Open since 2013.
"You are very good", Nadal said.
"I'm very sorry for Dominic", Nadal added.
"I just (kept) going, I'm very sorry for Dominic, he's a close friend on tour, a great guy, and I wish him all the very best".
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"(I am) sad for him because when [he arrived at] this moment, he did all the things well to win the match. Until the fifth-set tiebreaker, the first contested so far this tournament, it was truly any man's game to win. He is a fighter with a great attitude so that is the most important thing. He will have his chances in the future without a doubt, ' Nadal said.
World No. 1 Nadal saw off a battling Nikoloz Basilashvili, the first Georgian in a fourth round in NY, 6-3, 6-3, 6-7 (6), 6-4.
"Thank you for the all the support", he said, addressing the Arthur Ashe crowd.
The disappointment of failing to create a first match point seemed to weigh on him in the tiebreak and he played it dreadfully, showing rare confusion in going 0-3 down and then losing it 7-4.
Thiem, who lost to Nadal in the French Open final but had beaten the Spaniard three times in 10 previous meetings, struck 74 winners, including 24 with his stylish single-handed backhand, to keep the champion under constant pressure. Thiem is a top-10 player himself (he's now ranked No. 9), a star in his own right who some consider to be the heir apparent to Nadal. He came within two points of victory late in the fourth set before being pushed to a fifth, where he was two points from a loss.
"I tried to win a couple of points, couple of games, and just wait out what could happen ..."
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After holding at love in game 11, Rafa converted the third set point with a forehand down the line victor for four games in a row and 7-5, moving a set away from the place in the semi-final.
"If we skip the first set, it was a really open match from beginning to the end". And I played against a great opponent.
Those choruses resonated in the arena after key points, such as each time del Potro erased one of Isner's break chances, three in all.
Nadal has the best part of two days to recover before a semi-final against Juan Martin Del Potro, while the world No 9 left a stadium largely drained of spectators with nothing more than a reminder of his opponent's incredible fighting qualities.
Despite that, the 29-year-old was never broken in the 3 hour 31 minute match where Isner unleashed 26 aces but was undone by 52 unforced errors compared to Del Potro's 14.
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