Of the trio, Serena Williams was the most tested — saving set points on her way to a 7-5 6-0 win over former world number two Vera Zvonareva on Rod Laver Arena. 

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Zvonareva, now ranked 203rd, has experienced long lay-offs to injury and illness in recent years, but her first-set display wound back the clock to 2010 - the season of her highest ranking and two major final appearances. 

But the current world number one wound the clock forward in the second set — eventually dispatching of the Russian with relative ease. 

Just finishing as her sister started, 18th seed Venus Williams cantered to a 6-2 6-2 victory over Lauren Davis on Hisense Arena. 

In a rematch of their Auckland semi-final earlier in January, the elder Williams sister trailed by a break of serve in both sets but dominated the remainder. 

Radwanska, seeded sixth, was the first off court however — as she dispatched of Johanna Larsson 6-0 6-1 in 44 minutes on centre court. 

Larsson’s previous two major defeats have seen her win just two games in four sets, after she was thrashed in the US Open third round in 2014 by Jelena Jankovic 6-1 6-0. 

Dominika Cibulkova had a much easier time of progressing than in her first-round affair, thrashing Tsvetana Pironkova 6-2 6-0.

The 2014 finalist trailed by a set to Kirsten Flipkens in round one, but cruised to victory in one hour and 13 minutes on Thursday. 

Varvara Lepchenko, the 30th seed, ousted local hope Ajla Tomljanovic 6-1 7-6 (7-1), setting up a third-round battle with Radwanska. 

Alize Cornet, the 19th seed, overcame a stern challenge from qualifier Denisa Allertova, winning 6-4 6-7 (2-7) 6-2. 

Australian 29th seed Casey Dellacqua, though, bowed out after a promising start against Madison Keys. 

Keys turned around her woeful first-set form, which saw her hit 17 unforced errors, to canter to a 2-6 6-1 6-1 triumph. 

Garbine Muguruza, seeded 24th, won an undulating affair over veteran Daniela Hantuchova 6-1 1-6 6-0.

Muguruza will next face Timea Bacsinszky, who came from behind to beat American qualifier Anna Tatishvili 6-7 (5-7) 6-3 6-2. 

Elina Svitolina edged Nicole Gibbs in a tight clash 7-6 (7-3) 7-6 (8-6) as the 26th seed progressed to the third round in Melbourne for the second consecutive year. 

Venus Williams will play Camila Giorgi next after the Italian downed Tereza Smitkova 6-1 6-4.