Ranked No 80, Wang will go up against the winner of the match between No 20 seed Victoria Azarenka from Belarus and Frenchwoman Clara Burel in the next round.
Chinese player Wang advanced to this round after Greek Maria Sakkari, the No 9 seed, retired in their match (6-2).
Parry, who is ranked No 60, secured a victory against Chinese player Xiyu Wang (7-6 (2), 7-6 (5)) in the first round.
Here are the latest second-round results from the US Open (USTA Billie Jean King National Tennis Center, hard court, $75,000,000 prize money):
- Caroline Wozniacki vs. Renata Zarazua
- Naomi Osaka vs. Karolina Muchova
- Elena Rybakina vs. Jessika Ponchet
- Elisabetta Cocciaretto vs. Anastasia Pavlyuchenkova
- Sofia Kenin vs. Jessica Pegula
- Iga Swiatek vs. Ena Shibahara
- Karolina Pliskova vs. Jasmine Paolini
- Varvara Lepchenko vs. Anastasia Potapova
- Beatriz Haddad Maia vs. Sara Sorribes Tormo
- Katie Boulter vs. Jessica Bouzas Maneiro
- Caroline Dolehide vs. Sara Errani
- Marie Bouzkova vs. Liudmila Samsonova
- Mirra Andreeva vs. Ashlyn Krueger
- Yulia Putintseva vs. Xinyu Wang
- Anna Bondar vs. Anna Kalinskaya
- Clara Tauson vs. Diana Shnaider
- Tatjana Maria vs. Coco Gauff
- Victoria Azarenka vs. Clara Burel
- Peyton Stearns vs. Daria Kasatkina
- Donna Vekic vs. Greet Minnen
- Elina Svitolina vs. Anhelina Kalinina
- Emma Navarro vs. Arantxa Rus
- Lucia Bronzetti vs. Aryna Sabalenka: Wednesday
- Ekaterina Alexandrova vs. Iva Jovic: Wednesday
- Harriet Dart vs. Marta Kostyuk: Wednesday
- Qinwen Zheng (7) beat Erika Andreeva: 6-7 (3), 6-1, 6-2
- Madison Keys (14) beat Maya Joint (Q): 6-4, 6-0
- Elise Mertens (33) beat Ajla Tomljanovic: 6-3, 6-2
- Jule Niemeier beat Moyuka Uchijima: 6-4, 6-0
- Paula Badosa (26) beat Taylor Townsend: 6-3, 7-5
- Elena-Gabriela Ruse (Q) beat Barbora Krejcikova (8): 6-4, 7-5
