The unseeded Poles defeated their fifth-seeded opponents 6-7, 6-4, 6-4 in a closely contested match lasting two hours and 33 minutes.
Mladenović is a highly decorated doubles player with seven Grand Slam titles. Her most recent came at this year's Wimbledon, when she won the title alongside Guo.
Chwalińska and Linette will next face either Russia's Alina Korneeva and the Czech Republic's Darja Vidmanova or Hungary's Anna Bondar and Ukraine's Anhelina Kalinina.
Both Chwalińska and Linette were earlier eliminated in the first round of the US Open singles tournament.
Another Polish player, Katarzyna Piter, also competed in the US Open women's doubles alongside Czech partner Anna Siskova. They lost 3-6, 2-6 to Russia's Yelena Pridankina and China's Qianhui Tang in the first round.
Meanwhile, Poland's Iga Świątek reached the third round of the women's singles at Flushing Meadows with a 6-3, 6-2 win on Thursday over Argentina's Nadia Podoroska.
She will next face the Czech Republic's Marie Bouzková at the final Grand Slam tournament of the year.
Świątek, the 2022 US Open champion, is seeking her seventh Grand Slam singles title in New York.
The 25-year-old is the last Polish singles player remaining in the tournament after countrywomen Chwalińska, Linette and Magdalena Fręch all crashed out in the first round.
On the men's side, Poland's Hubert Hurkacz and Kamil Majchrzak were both eliminated in the second round.
The 2026 US Open runs until September 13.
(gs)
Source: Eurosport, IAR/PAP