The Ukrainian next plays either Venus Williams or Anna-Lena Groenefeld, who played later Tuesday.
Another qualifier also advanced when Tsvetana Pironkova beat teenager Alize Cornet 6-2, 6-1. The Bulgarian next plays third-seeded Dinara Safina, who had a bye into the second round, along with the other top three players in the tournament - Serena Williams, Jelena Jankovic and Elena Dementieva.
Marion Bartoli of France advanced by beating Dominika Cibulkova of Slovakia 6-3, 6-1 and Victoria Azarenka wasted a 5-2 lead before overcoming Agnes Szavay 7-5, 6-3.
The indoor tournament has brought together eight of the top 10 players in the world, with only Ana Ivanovic and Maria Sharapova missing.
Jankovic advances to Pan Pacific Open quarters
Scolari: Robinho Will Make A Difference
Jankovic advances at Pan Pacific Open
