Fifth seed Thiem won 7-6 (7-3) 7-6 (7-4) 4-6 7-6 (8-6) at Melbourne Park.
Thiem missed two match points before taking a third to win in four hours and 10 minutes.
READ ALSO: Alexander Zverev beats Stan Wawrinka to reach Australian Open semis
The 26-year-old will now face Germany’s Alexander Zverev on Friday – a first semi-final in Melbourne for both men.
Either Serbia’s defending champion Novak Djokovic or Swiss third seed Roger Federer will await the winner in Sunday’s final.
Thiem missed the chance to serve out the match at 5-4 in the fourth, becoming jittery with three unforced errors and a double fault as Nadal levelled by doing little to earn it.
But Thiem regrouped to win the third tie-break of a thrilling contest against the 19-time Grand Slam champion.
“I was holding my serve great and then it came to 5-4,” Thiem said.
“That was a special situation for me, serving against Rafa for a place in the Australian Open semi-finals for the first time.
“It was a mentally tough situation but I turned it around again in the tie-breaker.”
Thiem raised both arms in the air when Nadal hit a forehand into the net on the third match point, clutching and shaking his head in what was likely to be a mixture of relief and disbelief.
READ ALSO: Garbiñe Muguruza sets up Australian Open semi-final with Simona Halep
Nadal’s defeat means he will have to wait to be able to equal Federer’s all-time record of 20 Grand Slam victories.
Source: bbc
