They did it in different ways but Venus Williams and Agnieszka Radwanska both registered wins in Melbourne on Saturday.
The Williams sisters battled into the Australian Open fourth round as Agnieszka Radwanska also progressed at Melbourne Park.
Serena Williams recovered from yet another slow start to beat Elina Svitolina in three sets.
The American world number one eventually defeated Svitolina 4-6 6-2 6-0 in their third-round clash on Rod Laver Arena.
But she was sluggish early on and started slowly, just like she did on her way to trailing Vera Zvonareva 5-3 in her second-round victory.
In the end, Serena Williams found some of her best form and overpowered talented Ukrainian 20-year-old Svitolina " hitting 45 winners.
She will face Garbine Muguruza after the Spanish 24th seed beat Timea Bacsinszky 6-3 4-6 6-0.
Muguruza thrashed Serena Williams 6-2 6-2 at the French Open last year.
Venus Williams looked down and out against Camila Giorgi, trailing by a set and staring at a 5-2 deficit in the second.
But the American 18th seed fought her way back to claim a 4-6 7-6 (7-3) 6-1 win over the powerful Italian on Margaret Court Arena.
Giorgi led 4-2 in the second set and had Venus Williams serving at 0-40 but she failed to capitalise.
While Venus Williams reached the fourth round of a major for the first time since Wimbledon in 2011, Giorgi finished with 16 double faults and 62 unforced errors.
Radwanska had a far more comfortable win and will meet Venus Williams.
The Polish sixth seed had lost her previous two meetings with American Varvara Lepchenko but proved too good on Rod Laver Arena in a 6-0 7-5 victory.
Last year's runner-up Dominika Cibulkova booked her place in the fourth round with a 7-5 6-2 win over Frenchwoman Alize Cornet.
Next up for Cibulkova is unseeded two-time champion Victoria Azarenka, who battled past Barbora Zahlavova Strycova 6-4 6-4.
Madison Brengle continued her best-ever grand slam run, thrashing American countrywoman Coco Vandeweghe 6-3 6-2.