Świątek, a former world number one, on Tuesday eased past France's Varvara Gracheva 6-4, 6-1 in the second round of the hard-court tournament in the Chinese capital.
The 32-year-old Linette, meanwhile, reached the tournament's round of 16 with a walkover win against American Jennifer Brady on Monday.
The 2023 China Open runs until October 8.
Poland's Świątek last month lost her world No. 1 spot in women's tennis to Belarusian Aryna Sabalenka.
The 22-year-old Pole, coached by countryman Tomasz Wiktorowski, had topped the world rankings for 75 consecutive weeks, after taking over from Australian Ash Barty on April 4, 2022.
(gs)
Source: IAR, PAP