Men's champion Bernard Tomic, however, followed up the exploits of 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's title defence lasted just 92 minutes when she was dumped out 7-5 6-2 by American qualifier Bethanie Mattek-Sands, while Wozniacki, who struggled in her first round match on Monday, was beaten 6-4 7-6 (9-7) by Czech Lucie Safarova.
World number five Radwanska had won the Sydney title last year as part of a 13-match unbeaten streak that ended in the Australian Open quarter-finals said she was not overly concerned with her early loss.
"I really had a lot of good matches last week," the 24-year-old Pole added in reference to winning all three matches at the Hopman Cup in Perth last week.
"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.
"I think every week is different story. You start over and over again.
"Every tournament isn't the same thing. You're not winning every week every match. Normally you just to have to start again, not really think what was happening in the last week."
Mattek-Sands will now face fellow American Madison Keys in the quarter-finals.
Former Wimbledon champion Petra Kvitova will play Safarova in the quarter-finals after the second seed smashed American qualifier Christina McHale 6-1 6-0 in a little over an hour.
Wozniacki, who missed the Brisbane tournament last week with a sore shoulder, said she was feeling fine on Tuesday but had failed to win the crucial points in the clash against Safarova.
"I felt like it was pretty good today. It was small things that I didn't win," the Dane said.
"I don't feel anything in my shoulder anymore. It's great. I've felt good for the last few days.
"I played two matches here then I get a few days over there (Melbourne) and get to play a few sets as well with some of the girls and with different types players.
"I should be ready for Melbourne."
Australian 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 defeating Roger Federer in the final on Sunday and he said he felt he would need the week off to recover properly for the season-opening grand slam.
"At the moment it's just all about recovery for me," Hewitt told reporters on Tuesday. "When you get older it gets a bit tougher than when you were 16.
"We're going into the first major and you've got to do what's absolutely right for you."
His place in the eight-man field will be taken by compatriot Jordan Thompson, who will play world number nine Richard Gasquet in their first matches on Wednesday. World number eight Tomas Berdych opens the tournament against Spain's Fernando Verdasco.
Verdasco's compatriot David Ferrer was given a traditional Maori welcome at the Auckland Open on Tuesday in recognition of his contribution to the tournament.
Ferrer will be making his 10th appearance at the tournament, having won four titles, including the last three in succession.
"Thank you very much for everything," the world number three told the packed crowd at the Auckland Tennis Centre after being presented with a manaia (Maori carving).
"This tournament is very special. I hope to come back for a lot more years and try to win one more time."
Ferrer will meet qualifier Donald Young in the second round on Wednesday after the American beat Argentina's Federico Delbonis 7-5 6-2.
Former champion Philipp Kohlschreiber also advanced to the second round with a tough 6-2 3-6 7-5 victory over Spain's Pablo Carreno Busta.
WTA Tour results
WTA Sydney - Round 2
3-Sara Errani (Italy) beat Lauren Davis (U.S.) 7-5 6-2
Lucie Safarova (Czech Republic) beat 6-Caroline Wozniacki (Denmark) 6-4 7-6(7)
Tsvetana Pironkova (Bulgaria) beat Varvara Lepchenko (U.S.) 6-3 6-2
Carla Suarez Navarro (Spain) beat Ekaterina Makarova (Russia) 7-6(4) 6-3
2-Petra Kvitova (Czech Republic) beat Christina Mchale (U.S.) 6-1 6-0
Madison Keys (U.S.) beat Ajla Tomljanovic (Croatia) 6-0 3-6 7-6(3)
Bethanie Mattek-Sands (U.S.) beat 1-Agnieszka Radwanska (Poland) 7-5 6-2
5-Angelique Kerber (Germany) beat Kaia Kanepi (Estonia) 6-3 6-4
WTA Hobart - Round 2
Alison Riske (U.S.) beat Casey Dellacqua (Australia) 7-5 4-6 6-3
WTA Hobart - Round 1
3-Elena Vesnina (Russia) beat Monica Puig (Puerto Rico) 6-4 6-4
Storm Sanders (Australia) beat Peng Shuai (China) 6-2 6-2
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- Svetlana Kuznetsova