Świątek, 25, beat American Ashlyn Krueger 6-1, 6-4 in the third round, while Chwalińska, 24, rallied past another American Iva Jovic 6-4, 6-1.
Świątek, ranked seventh in the world, will face 31st-ranked American Ann Li for a place in the semifinals.
Chwalińska's next opponent will be Greece's Maria Sakkari.
Świątek's victory against Krueger keeps alive her hopes of qualifying for the season-ending eight-player WTA Finals, which will take place from November 8 to 15 in Indian Wells, California.
The Wuhan Open runs until Sunday.
(gs)
Source: IAR/PAP