Thompson saved three match points in the second set before overcoming an increasingly fatigued Nadal 5-7, 7-6(6), 6-3 in a gruelling encounter that finished just before midnight on Pat Rafter Arena.
Thompson booked a semi-final against Bulgarian Grigor Dimitrov with the win, while at the same time throwing a spanner in the works of Nadal's Australian Open preparations.
Nadal said he had plenty of chances to win, but just couldn't take them.
"I think he played a good match. For me, it was not the best match, I had a lot of opportunities to win it," he said.
"I need to accept that. After a year (of not playing), that's normal."
Playing his first tournament after almost 12 months away from the sport through injury, Nadal appeared headed for a straight sets win after claiming the first set and then getting to a 6-4 lead in the second set tiebreak.
But an inspired Thompson refused to go away and took advantage of some unforced errors from the Spaniard to clinch the second set.
Nadal, who was broken early in the third set, took a medical time out at 1-4 down after appearing to need treatment to his upper left thigh.
He was able to continue but was unable to break back and Thompson held on to the delight of the capacity crowd.
Nadal said he wouldn't know how bad the injury was until the next day.
"A lot of things can happen in a body like my body after a year without playing tennis," he said. "So hopefully it is just a muscle that is supercharged."
Thompson said he was so wrapped up in the match he couldn't remember a key moment.
"I completely forgot I saved match points," Thompson said immediately afterwards.
"To beat Rafa in Brisbane in a quarter-final, and I think it is now my first semi-final on a hard court, I couldn't be happier."
Thompson will now play second seed Dimitrov in the semi-finals after the Bulgarian's 6-1, 6-4 victory over Australian Rinky Hijikata.
The second semi-final sees top-seeded Dane Holger Rune up against Russian Roman Safiullin.
Rune looked in great touch as he downed Australian qualifier James Duckworth 6-2, 7-6(6), while unseeded Safiullin beat Italy's Matteo Arnaldi 7-6(4), 6-2.
Nadal had gone into his quarter-final against Thompson in superb touch following relatively easy wins in his opening two rounds.
But Thompson, the world number 55, ensured that the Spaniard wouldn't have it all his own way, returning well throughout to constantly pressure Nadal's serve.
Despite losing his serve for the first time this tournament at 3-3 in the opener, Nadal was able to break Thompson twice to clinch a tight first set in 70 minutes.
Thompson threw everything at Nadal in the second set, playing some superb tennis, but the Spaniard was able to somehow absorb the pressure.
It looked like vintage Nadal as he turned the screws in the tiebreak, opening a 3-0 lead.
But Thompson came back to level at 3-3, then saved two match points at 6-4 down, clinching the set in 83 minutes.
Nadal began to look tired at the start of the third set, in contrast to the Australian, and it came as no surprise when he was broken early in the third, with Thompson comfortably holding on.
Sabalenka fires warning
In the women's draw, Aryna Sabalenka fired a warning ahead of her Australian Open defence by powering into the semi-finals with a straight-sets demolition of Daria Kasatkina.
Sabalenka's 6-1, 6-4 victory was her 14th consecutive win on Australian soil after also claiming the Adelaide crown in the lead-up to last year's opening Grand Slam of the year.
The Belarusian raced through the first set against the Russian in 32 minutes, but had to fight harder in the second, breaking Kasatkina once and holding on to win the match in one hour and 26 minutes.
Sabalenka will now play fellow Belarusian Victoria Azarenka with a 2023 Australian Open final replay against second seed Elena Rybakina a possibility for Sunday's decider.
Former Grand Slam champions Azarenka and Rybakina reached the semis in contrasting fashion.
Two-time Australian Open winner Azarenka took two hours and 30 minutes before finally outlasting third-seeded Latvian Jelena Ostapenko 6-3, 3-6, 7-5 in the first match on Pat Rafter Arena.
Rybakina was then handed a spot in the last four when her Russian opponent Anastasia Potapova withdrew with a stomach problem after losing the first set 6-1.
Rybakina will face Linda Noskova next after the Czech player saw off 16-year-old Russian Mirra Andreeva 7-5, 6-3.
