Nadal, seeking an 18th Grand Slam title, recovered from losing the first set 6-0 to record an epic 0-6, 6-4, 7-5, 6-7, 7-6 triumph in a match which finished past 2am local time.

The 32-year-old top seed will next face Argentina's Juan Martin del Potro following his victory over Thiem, achieved after four hours and 49 minutes of gruelling action on Arthur Ashe Stadium at Flushing Meadows.

"I said to Dominic: 'I'm very sorry and keep going,'" said Nadal.

"He has plenty of time to win. 

"He will have his chances in the future without a doubt."

Del Potro, who won the event in 2009, reached the semi-finals by defeating John Isner of the United States 6-7, 6-3, 7-6, 6-2 amid stifling conditions.

He will clash with Nadal in the last four on Friday (September 7).

In the women's draw, Williams continued her pursuit of a record-equalling 24th Grand Slam crown after she dispatched Czech eighth seed Karolína Plíšková 6-4, 6-3 to book her place in her ninth consecutive semi-final.

The 36-year-old American will take on Anastasija Sevastova of Latvia, who knocked out defending champion Sloane Stephens with a comfortable 6-2, 6-3 win.

"I don't think I have another 10 years of having opportunities to be able to play and win championships," said Williams.

"Every match really means a lot to me. I kind of go out there and I just do the best that I can."

The tournament is due to continue tomorrow.