Thiem, 26, topped the No. 1 seed 7-6 (3), 7-6 (4), 4-6, 7-6 (6) to book his first Grand Slam semi-final outside the French Open, sealing Nadal's second Australian Open quarter-final exit in his past three appearances.
Alexander Zverev will make his Grand Slam semi-final debut against the Austrian after he came from a set behind to beat Stanislas Wawrinka 1-6, 6-3, 6-4, 6-2.
Simona Halep was the first to book her spot in the semi-finals after she blitzed 28th seed Anett Kontaveit 6-1, 6-1 in less than one hour.
Her next opponent will be Garbine Muguruza, who is the only unseeded semi-finalist in either draw after defeating Anastasia Pavlyuchenkova 7-5, 6-3.
Wednesday's Quarter-Final Results
(7) Alexander Zverev bt. (15) Stanislas Wawrinka: 1-6, 6-3, 6-4, 6-2
(5) Dominic Thiem bt. (1) Rafael Nadal: 7-6 (3), 7-6 (4), 4-6, 7-6 (6)
(4) Simona Halep bt. (28) Anett Kontaveit: 6-1, 6-1
Garbine Muguruza bt. (30) Anastasia Pavlyuchenkova: 7-5, 6-3
Visit the Australian Open website to see the full results.
Thiem has made it to the semi-finals of Roland Garros on four occasions but never advanced as far in any of the three other majors in 18 previous attempts.
The Austrian ended that run with a memorable win over Nadal—who has twice beaten him in the French Open final—where he fired back to win the first two sets despite suffering the first break in each.
He suffered a slight setback but withstood the pressure to triumph in a third tiebreak in as many attempts against Nadal, who looked second best in his first defeat to Thiem at a major.
Zverev's prospects looked low coming into the Australian Open this year following a bumpy patch of form, including three straight defeats at the ATP Cup.
The German suggested after Wednesday's match that it was the lowered expectations that had spurred him to greater success after a period of "playing horrible" tennis, per The National's Reem Abulleil.
Zverev won just three of 19 receiving points he faced during a woeful opening set against Wawrinka.
Tennis Channel analyst Jon Wertheim commented as the German prepares to rejoin the elite ranks in the penultimate stage of a Grand Slam.
Halep will play in the Australian Open semis for a second time in her career, hoping she can better her runner-up finish to Caroline Wozniacki in the 2018 renewal.
The Romanian rampaged past Kontaveit in 53 minutes and saved the sole break point she faced in what was an efficient day's work.
The world No. 3 said in her post-match press conference that "perfection doesn't exist," despite being pleased with her performance in the quarter-finals.
Muguruza only learnt she'd be facing Halep after her own straight-sets quarter-final victory against Pavlyuchenkova, advancing to the Australian Open's last four for the first time in her career. She reached the quarters in 2017 but had failed to make it past the fourth round in six other appearances.
The two-time major winner hasn't reached the last four of a Grand Slam since her semi-final exit at the 2018 French Open, when it was Halep who beat her in straight sets en route to the Roland Garros title.
Halep will look to stop Muguruza from making a first major final appearance since she won Wimbledon in 2017, with the winner of their semi set to face either Ashleigh Barty or Sofia Kenin in Saturday's decider.