Radwanska overcame Puig 6-4 6-0 to secure a sixth successive fourth-round berth at Melbourne Park on Friday.
Agnieszka Radwanska passes Monica Puig test
Agnieszka Radwanska was too good for Monica Puig in the third round of the Australian Open, though there will be concerns about the fourth seed's fitness.
However, slightly concerning for Radwanska - who had to withdraw from the Sydney International due to a leg injury - was the fact she required medical attention on the same area on three occasions in the second set.
Puig came into the contest having played just three top-10 opponents previously in the form of Maria Sharapova, Angelique Kerber and Sara Errani, though she beat the latter at Wimbledon in 2013.
But the Puerto Rican was not overawed early, with some impressive groundstrokes seeing her stay level alongside Radwanska at 4-4 after exchanging breaks in the seventh and eighth games.
Puig then fended off a set point but she could not save another as Radwanska's poise and powerful hitting from the baseline helping her take charge.
And despite needing treatment in the second set, 2014 semi-finalist Radwanska still looked lively as she swept aside Puig with ease.
STATISTICAL BREAKDOWN
Radwanska [4] Puig 6-4 6-0
ACES
Radwanska - 1
Puig - 1
WINNERS/UNFORCED ERRORS
Radwanska - 17/11
Puig - 22/29
BREAK POINTS WON
Radwanska - 5/7
Puig - 1/4
FIRST SERVE PERCENTAGE
Radwanska - 64
Puig - 71
PERCENTAGE OF POINTS WON ON FIRST/SECOND SERVE
Radwanska - 78/30
Puig - 71/47
TOTAL POINTS
Radwanska - 61
Puig - 43
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