World number two Swiatek came from a set behind to defeat Caroline Garcia 6-7 (8/10), 7-6 (7/5), 6-1 in a match that hinged on two nail-biting tie-breaks.
Gauff, the US Open champion, comfortably disposed of world number six Maria Sakkari 6-2, 6-4.
Swiatek endured a tense opening set that Garcia -- ranked 10th -- eventually stole with a vicious passing shot at the end of a marathon tie-break.
The Pole was 4-1 up in set two but threatened a match-ending collapse against a stubborn Garcia, finally edging it when the Frenchwoman netted a limp backhand.
From there, Swiatek took control, notching a double break in the deciding set and finally taking match point at the fifth time of asking.
"For sure, it was really intense. We played really fast," the four-time Grand Slam winner told a post-match news conference.
"There was no time sometimes to think or analyse. I'm happy I used my intuition a lot," she said.
"I just knew that she was risking, so... her mistakes could come."
Gauff sailed through a rapid first set and made short work of her opponent in a dominant second, breaking serve in the fifth game.
She took the match by thundering down a meaty serve that Sakkari could only return wide.
In Friday's other quarter-finals, world number one Aryna Sabalenka will play fifth-ranked Elena Rybakina, while 17th-ranked Jelena Ostapenko faces Liudmila Samsonova of Russia.
The China Open is taking place for the first time since 2019 after Beijing ended strict zero-Covid travel curbs.
The men's competition concluded on Wednesday, when Italy's Jannik Sinner beat world number three Daniil Medvedev in the final.
