Halep, seeded third in the event, trailed 7-5, 2-0 before she halted the match.
Kalinskaya continued her success in Washington, as she reached the semifinals there as a qualifier in 2019. The women's tournament wasn't held in 2020 and 2021 amid the COVID-19 pandemic.
In other second-round matches, sixth-seeded Kaia Kanepi (37) of Estonia rallied past China's Lin Zhu (28) 4-6, 6-4, 6-4; Australia's Daria Saville (28) downed the American No. 1 seed Jessica Pegula (28) 7-5, 6-4; and Canada's Rebecca Marino (31) topped Germany's Andrea Petkovic (34) 6-3, 3-6, 6-1.
Mubadala Silicon Valley Classic
Second-seeded Paula Badosa (24) of Spain was pushed to the limit before emerging with a 6-2, 5-7, 7-6 (5) win over the United States' Elizabeth Mandlik (21) in the second round in San Jose, California.
Elsewhere in second-round action, the United States' Amanda Anisimova (20) upset eighth-seeded Karolina Pliskova (30) of the Czech Republic 3-6, 7-5, 6-1, and seventh-seeded Daria Kasatkina (25) of Russia eliminated the Unites States' Taylor Townsend (26) 6-4, 6-0.
Third-seeded Ons Jabeur (27) of Tunisia, who made the Wimbledon final last month, powered past the United States' Madison Keys (27), a former U.S. Open finalist, 7-5, 6-1.
