Nadal, the No. 1 seed and defending U.S. Open champion was completely gassed in a dominant 6-0 first-set sweep for Thiem.
But in a titanic battle worthy of a final, with stunning winners on both racquets and breathtaking defence, top seed Nadal rallied to outlast Thiem 0-6 6-4 7-5 6-7 (4-7) 7-6 (7-5) in the longest match of this year's tournament - four hours and 49 minutes.
"Suffering is the right word", Nadal said.
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.
It was the second time Nadal played a 4 hours + match, with his third round win over Karen Khachanov ending at 4 hours 23 minutes.
Nadal mounted an impressive comeback, winning the next two sets as he got to grips with the Austrian's power.
"Very demanding in all aspects", Nadal said later.
Thiem then grabbed a 4-3 lead in the third which he stretched to 5-3 but then it was his turn to crack as Nadal raced away with three games to claim a two sets to one lead. Yeah, it was [a] question of little bit of luck at the end.
"I was playing really not a good game", said Williams, who was a point from trailing 4-1 and did fall behind 4-2 while making 22 of her 30 unforced errors in the first set.
"He has plenty of time to win big tournaments and has everything".
This story was first published on CNN.com, "Rafael Nadal outlasts Thiem in 5-set US Open thriller". And I played against a great opponent.
"Forever I'm going to remember this match, for sure", Thiem said.
Having looked the more tired of the two, it was Nadal who was applying the greater pressure and at 5-5, 0-40 it seemed this was his chance. "I think he was also not on his top level in the first set, for sure not", Thiem said. Happy, of course, to be in semi-finals again, it means a lot to me. "The conditions were tough, very humid for me".
The Nadal who was gassed and wearing a cooling vest during breaks in the first set was no more.
Stiller felt the intensity of the match and was often seen displaying the kind of nerves he had while taking his lie detector test in "Meet the Parents". I am focused on trying to make that happen.
"He will say "this is my opportunity and I'm expected to lose, but I have to go out there guns blazing". Nadal then broke again to take the set 7-5.