Home favourite and top seed Barty had to come from a set down to progress in Melbourne, beating Lesia Tsurenko 5-7 6-1 6-1.
The Queenslander ensured she joined several other big names in advancing, with defending champion Naomi Osaka triumphing along with Serena Williams and Petra Kvitova - straight-sets winners over Anastasia Potapova and Katerina Siniakova respectively.
Venus Williams did not follow her sister into round two, though, as she fell to 15-year-old Coco Gauff once again.
Gauff had already beaten fellow American Williams at Wimbledon last year and pulled off a repeat on Monday.
Sloane Stephens crashed out 2-6 7-5 6-2 to Zhang Shuai, while Barbora Strycova lost to Sorana Cirstea in straight sets, but fellow seeds Petra Martic, Sofia Kenin and Ekaterina Alexandrova all advanced.
Caroline Wozniacki, who will retire at the end of the tournament, prolonged her career by easing past Kristie Ahn 6-1 6-3.