The match see-sawed throughout, eventually decided by a fifth set tie-breaker, with Nadal taking out the match 0-6, 6-4, 7-5, 6-7, 7-6.
Rafa finally started to play with more aggression in set number three, saving a break point at 2-2 before wasting two game points in game seven and allowing Thiem to break him with a return victor.
Thiem, on a roll, took the opening set in just 24 minutes, breaking Nadal thrice.
The two players met in the semis at last year's U.S. Open, a match Nadal won in four sets.
Thiem was also 5-3 ahead in the third set and 4-2 in the fourth before he was reeled in by Nadal, the three-time champion in NY.
"Very demanding, in all aspects", said Nadal, who will face 2009 champion Juan Martin del Potro on Friday for a berth in the final.
Having survived an epic against Karen Khachanov in the third round, Nadal again dropped a set to Nikoloz Basilashvili but recovered to win in four, while Williams was pushed to a deciding set for the first time by Kaia Kanepi.
"To reach the semifinal again here in NY in my favourite tournament is very special to me", said Del Potro after his eighth win over Isner in 12 meetings.
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McGuckin said he was in the mood to celebrate on Thursday but he anticipates his group's work is not done. Proponents will also be required to improve consultations with First Nations.
"It was a very tough start and then I tried to stay in the match in some way in that second set and I did".
Thiem pushed Nadal to break point in the ninth game. Isner is known for his marathon matches and played another long one in Louis Armstrong Stadium.
"One of my best matches ever", Thiem had said in an on-court interview. The southpaw went down a break in the third and fourth sets as Thiem simply never backed off from making winners off both the wings.
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.
His 12th appearance breaks the Ryder Cup record held by Nick Faldo.
This is the world number one's first meeting with Thiem at the US Open but he has faced the Austrian three times at Grand Slam level (all at the French Open), winning in straight sets on each occasion. "Have been a very tough start for me". After that first set, then the match became more normal. "I like this feeling, but at the same time you feel exhausted after that", Nadal said. Serving for the set at 5-3, Nadal got broken as well after a deep return from Thiem but he managed to clinch the set with another break in game 10, forcing an error from Dominic to level the overall score at 1-1.
"Still long way to go, I think", she said.
The 24-year-old (Thiem turned 25 on Monday) hit 42 winners and only 13 unforced errors while Anderson made more than double that number of unforced errors.