Defending champion Nadal lost the opening set 6-0 in NY as ninth seed Thiem looked to reach his first Grand Slam semi-final.
On the previous three such occasions, he'd lost. "Then I tried to stay in the match, in some way".
Thiem, meanwhile, has finally found some form after a post-clay court season malaise.
"I hope that it´s a little bit more comfortable on hard court, but I´m not sure". The ninth, however, proved costly: On Nadal's first match point, at 6-5 in the tiebreaker, Thiem misjudged an overhead smash, sending it into the back wall to end the match at 2:03 a.m. on Wednesday. "It means a lot to me".
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.
The fourth set was a wild 81-minute ride that began with Thiem facing break points, saw the Austrian threaten a double break before being pegged back and then a tired Nadal miss a chance to win the match.
"I have had three very nice experiences and seven terrible experiences", said Thiem, who has made the last-eight at a Slam other than Roland Garros for the first time.
"Wake up", Nadal said he told himself.
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Asked about that at his news conference, Thiem said with a chuckle: "Well, I don't think he's really sorry". I don't want to lose against anybody. 1 Novak Djokovic in the final. He saved 12 break points, including three while serving at 5-5, 0-40 in the fifth set.
Nadal ran into an inspired opponent for the second match in a row and was put through his paces by Nikoloz Basilashvili before eventually coming through 6-3, 6-3, 6-7, 6-4.
The depth and strength of Thiem's groundstrokes were doing what Nadal's shots usually do to opponents: robbing them of time and space. He was two points from victory at 6-5, deuce, in the fourth as Thiem served, but flubbed a forehand volley, leaping for a ball that appeared to be sailing out and dumping it into the net.
He paid tribute to the crowd, which kept up their vocal support of the three-time US Open champion despite the hours stretching into the early NY morning.
After the match the Spaniard said he was "sorry" for inflicting the defeat on the 25-year-old.
In the first Nadal was all over the place, totally unable to find any rhythm and a set down after just 26 minutes when he won just seven points.
Williams was on track to meet defending champion Sloane Stephens in the semi-finals but her third-seeded countrywoman was dumped out of the tournament via a 6-2, 6-3 loss to 19th seed Anastasija Sevastova.
Del Potro, the 6-foot-6 (1.98m) Tower of Tandil knows it will be a battle against 6-foot-10 (2.08m) Isner, who has blasted a tournament-leading 112 aces.