World number one Ash Barty won her first WTA Tour match in almost a year at the Yarra Valley Classic, while Naomi Osaka got her Gippsland Trophy campaign going with a victory.
Barty sat out the vast majority of the 2020 season due to the coronavirus pandemic but marked her comeback with a 6-3 6-3 success over Ana Bogdan at Melbourne Park.
The Australian will face Marie Bouzkova next after the Czech defeated Aliona Bolsova on Tuesday.
Garbine Muguruza raced past Alison Van Uytvanck 6-2 6-0 and she was joined in the third round by Petra Kvitova, who battled to beat Venus Williams 7-6 (8-6) 7-5.
Reigning Australian Open champion Sofia Kenin, who was 7-5 up when Camila Giorgi retired from their match, is also through.
In her first match since winning the US Open in September, Osaka cruised to a 6-2 6-2 success against Alize Cornet and will meet Katie Boulter after the Briton came from a set down to beat Coco Gauff 3-6 7-5 6-2.
Iga Swiatek was also making her first appearance since winning a major title – the French Open last October – and after a slow start won 10 of the final 11 games to beat Kaja Juvan 2-6 6-2 6-1.
Aryna Sabalenka ended 2020 with back-to-back titles in Ostrava and Linz, before kicking off the new year with another trophy in Abu Dhabi. However, her run of 15 straight victories ended with a 1-6 6-2 1-6 loss to Kaia Kanepi.
Bianca Andreescu was due to gear up for the Australian Open by contesting the Grampians Trophy this week but withdrew from the competition to focus on training instead.