The 11th-seeded Badosa - who briefly dropped out of the world's top 100 in early 2024 as she battled a debilitating back injury - proved too good for No.3 seed Gauff in their quarter-final encounter, winning 7-5 6-4 in a match lasting one hour and 43 minutes.
The prize for Badosa is a maiden grand slam semi-final, where she will take on either two-time defending champion Aryna Sabalenka or Russian veteran Anastasia Pavlyuchenkova.
Gauff was riding a 13-match winning streak coming into the Rod Laver Arena clash, but she was no match for the inspired 27-year-old.
Coco Gauff was well below her best in a shock loss to Paula Badosa. (Lukas Coch/AAP PHOTOS)
"I've been through a lot," Badosa in her on-court interview.
"In the past I was one of the best players in the world but I think now I'm a better player, more mature.
"I think I managed my emotions a little bit better."
Badosa claimed the only break of the opening set in the 11th game.
She set up the crucial break-point opportunity by nailing two clutch volleys to go up 30-40 and then converted the advantage with a forehand cross-court winner.
The Spaniard served the set out in the following game with a minimum of fuss.
Badosa looked to have taken a stranglehold on the match when she broke again in marathon opening game of the second set that lasted for 14 minutes.
The American did manage to get the set back on serve at 2-2 only to be broken again immediately after leading 40-15.
And things only got worse for the 20-year-old who double-faulted to give Badosa the double break and a 5-2 lead.
Gauff got one of the breaks back but Badosa held her nerve to serve it out at the second attempt.
"As you know, I'm a very emotional person," said the winner.
"I came in, I wanted to play my best game. I think I did it.
"Coco at the beginning, she was playing insane tennis, but I'm super proud of the level I gave today."
Badosa's previous best results at the majors were quarter-finals at the 2021 French Open and last year's US Open.
Both she and Gauff had only dropped only one set in their previous four matches at the Open.
"A year ago I was here with my back and I didn't know if I would have to retire from this sport," said Badosa, the one-time world No.2 and former French Open junior champion.
"Now I'm here playing against the best in the world.
"I won today and I'm in the semi-finals."
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