Wozniacki eased to a 6-2 6-2 victory over Petra Martic at the WTA International event in New Zealand, where the Dane was a runner-up to Venus Williams in 2015.
Her opponent in the last eight will be teenager Sofia Kenin, who won a tie-break in the second set to get past fellow American Varvara Lepchenko.
Radwanska, the 2013 champion and this year's fourth seed, defeated another American, Taylor Townsend, 6-3 7-5 to advance.
Sachia Vickery overcame Veronica Cepede 6-2 6-4 and will take on Radwanska next.
She was joined in the next round by German second seed Julia Goerges, a straight-sets winner over Viktoria Kuzmova.
Barring 2016 finalist Goerges' path to the last four will be Polona Hercog, the Slovenian having accounted for veteran Kirsten Flipkens 6-4 6-2.