The No. 5-seeded Thiem won the match 7-6 (3), 7-6 (4), 4-6, 7-6 (6) in 4:10 to advance and face Germany's Alexander Zverev in a men's semifinal. The winner will face the victor of the other semifinal between No. 3 Roger Federer and No. 2 Novak Djokovic in the men's final.
"It's the first time I'll play in a Grand Slam semifinal and I'm the older player," Thiem said of his upcoming match against the 22-year-old Zverev, the tournament's No. 7 seed. "We are great friends, I'm really happy he is playing in his first semifinal."
Thiem fired 14 aces, compared to Nadal's 11 in Wednesday's win. He also had more unforced errors and double faults than Nadal, and hit 65 winners in the triumph.
Nadal and Thiem exchanged points in the first game before Nadal won the seventh and eight games to take a 5-3 lead in the set. Thiem responded by winning the next two games to tie the set, before Nadal won the 11th game. Thiem climbed back with an ace in the 12th game to tie the set at 6-6 and won the tiebreak with a forehand winner.
Thiem held a 2-1 lead in the second set before Nadal won three consecutive games to take a 4-2 edge. Thiem then won three straight games before Nadal tied the set at 5-5. Thiem and Nadal exchanged game wins before Thiem won the tiebreak with another forehand winner.
With Thiem leading 2 sets to none, they played to a 4-4 tie in the third before Nadal won the final two games to take the set and climb back into the match.
Thiem lost the first game of the fourth set on a forehand unforced error, but responded by winning the next three games. The world No. 1 rallied with three consecutive games to take a 6-5 edge before Thiem forced a tiebreak, and eventually won match point on a Nadal forehand unforced error. The loss ended Nadal's bid to win his first Australian Open since 2009.
Federer advanced to the semifinals by beating American Tennys Sandgren in five sets. Djokovic -- the defending champion -- beat Canadian Milos Raonic in straight sets to set up a clash with Federer. Zverev beat 15th-seeded Stan Wawrinka in four sets to advance to the semis.
Federer is looking to win his seventh title in Melbourne. Djokovic has seven Australian Open titles and Zverev is making his first semifinal appearance in a Grand Slam.
The women's semifinals feature No. 1 Ashleigh Barty against No. 14 Sofia Kenin and No. 4 Simona Halep against Garbine Muguruza.
"I expect a very difficult match, but it's the semifinals so it should be like that," Halep said. "I'm all in. I'm confident."
The Australian Barty won the 2019 French Open, but is making her first semifinal appearance in Melbourne. Kenin is making her first Grand Slam semifinal appearance. Halep, who the French Open in 2018 and Wimbledon last year, advanced to the Australian Open final two years ago before losing to Caroline Wozniacki. Muguruza -- a two-time Grand Slam winner -- is making her first semifinal appearance in Melbourne.