The world number one kept alive his bid for a fourth title in New York and 18th Grand Slam crown on track in a sizzling 4-hour 49-minute contest which concluded at 2.04 a.m. on Wednesday.
However, the 32-year-old was fortunate to triumph on another hot and humid night at Flushing Meadows, 24 hours after Roger Federer had been dumped out of the tournament by John Millman.
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.
“I suffered, that’s the right word,” said Nadal after playing his longest ever match at the tournament.
“I said to Dominic I am sorry. He’s a great guy, a close friend who will have many more opportunities to win the big titles.
“He has a great attitude and is a great fighter.”
In a dramatic final set, Nadal saw five break points come and go before Thiem went long with a smash on the first match point.
It was his 58th unforced error on a night when he sent down 18 aces and fired 58 winners.
The semi-final will pit Nadal against third seed Juan Martin del Potro for the second successive Grand Slam.
At Wimbledon, Nadal came back from two sets to one down to win in five in a quarter-final which stretched to almost five hours.
Thiem broke three times in a 24-minute first set, handing Nadal just his third ‘bagel’ at a Grand Slam.
The top seed won just seven points in the opener.