World number one Iga Swiatek needed just 55 minutes to beat Spanish qualifier Cristina Bucsa and breeze into the Australian Open fourth round.
Third seed Jessica Pegula also enjoyed a speedy victory on Friday, taking 65 minutes to beat Marta Kostyuk 6-0 6-2.
Seventh seed Coco Gauff advanced with a 6-3 6-2 victory over American compatriot Bernarda Pera.
Reigning French and US Open champion Swiatek said of her challenging meeting with Rybakina: "We know each other pretty well. For me it doesn't really matter who it's against. I just want to stay focused on myself."
Pegula will face 2021 French Open singles champion Barbora Krejcikova for a place in the quarter-finals, while Gauff plays 2017 Roland Garros winner Jelena Ostapenko.
Czech Krejcikova beat Ukraine's Anhelina Kalinina 6-2 6-3, while Latvia's Ostapenko claimed a 6-3 6-0 win against Kalinina's compatriot Kateryna Baindl.
Rybakinabeat last year's Melbourne finalist Danielle Collins 6-2 5-7 6-2, with two-time Australian Open champion Victoria Azarenka also in action later on day five at Melbourne Park.