Defending champion and third seed Caroline Wozniacki beat Johanna Larsson at Melbourne Park on Wednesday.
Simona Halep reached the final of last year's Australian Open, but the top seed says she does not feel any pressure this year.
Daria Kasatkina was the highest-ranked seed to be beaten on day two of the women's singles at Melbourne Park, but Simona Halep had a scare.
Kaia Kanepi looked capable of inflicting another grand slam defeat on Simona Halep, but the Australian Open's top seed fought back superbly.
Victoria Azarenka said she was "struggling" following her early exit at the Australian Open, adding: "My confidence level is not there."
Eugenie Bouchard's reward for beating Peng Shuai is a second-round meeting with Serena Williams at the Australian Open, and she's excited.
Victoria Azarenka made her first Australian Open appearance since 2016, though it ended in an opening-round defeat on Tuesday.
Serena Williams, who is seeking an eighth Australian Open title, revelled in her 6-0 6-2 demolition of Tatjana Maria in Melbourne.
Serena Williams completely overpowered Tatjana Maria 6-0 6-2 in a one-sided first-round affair at Melbourne Park on Tuesday.
Maria Sakkari caused a major upset on day one at the Australian Open as she beat 2017 French Open champion Jelena Ostapenko.