However, Bernard Tomic, the men's champion, followed up the exploits of his fellow Australian Marko Matosevic, who earlier beat Florian Mayer 6-2, 4-6, 6-3, to demolish eighth seed Marcel Granollers 6-3, 6-0 in just under an hour.
Radwanska and Wozniacki followed past grand slam title winners Svetlana Kuznetsova and Francesca Schiavone and Jelena Jankovic, a former world No.1, as early departees.
Radwanska's title defence lasted just 92 minutes when she was dumped out 7-5, 6-2 by the American qualifier Bethanie Mattek-Sands, while Wozniacki, who struggled in her first-round match on Monday, lost 6-4, 7-6 (9-7) to the Czech, Lucie Safarova.
"I really had a lot of good matches last week," said Radwanska, the world No.5, who had won the Sydney title last year as part of a 13-match unbeaten streak. "It's not like I'm playing bad. I'm not worried about that. I just think not my day [and] ... sometimes you have to lose."
Mattek-Sands will now face her fellow American Madison Keys in the quarter-finals.
Petra Kvitova, the former Wimbledon champion, will play Safarova in the quarter-finals after the second seed smashed Christina McHale, an American qualifier, 6-1, 6-0.
Wozniacki, who missed the Brisbane tournament last week with a sore shoulder, said she was feeling fine yesterday but failed to win the crucial points against Safarova. "I felt like it was pretty good today. It was small things that I didn't win," said the Dane. "I should be ready for Melbourne."
Australia's Lleyton Hewitt took a different approach to being ready for the Australian Open by withdrawing from the invitational Kooyong Classic tournament in Melbourne.
The 32-year-old caused a major upset at the Brisbane International by defeating Roger Federer in the final on Sunday and said he felt he would need the week off to recover properly for the season-opening grand slam.