Top seed Wozniacki served for the match at 5-4 in the second set before Poland’s Radwanska hit a purple patch to run away with victory.
Radwanska, the world No 8, will play Belarus’s world No 3, Victoria Azarenka, in the semi-finals.
World number two Kvitova lines up against China’s world number five Li Na.
Wozniacki, teary-eyed during the final set, floated a forehand long to concede defeat just after midnight.
She faces the prospect of starting the Australian Open as the top seed having relinquished the world No 1 spot between the draw and play getting under way at Melbourne Park.
Kvitova is guaranteed to knock Wozniacki off the top if she wins the final in Sydney, scheduled for Friday night.
“I don’t think about the ranking,” said Wozniacki, who has never won a grand slam.
"The most important thing is to be healthy and be able to play and play well.”
Kvitova was highly impressive in her 6-0 6-4 thumping of Slovakia’s Daniel Hantuchova on Ken Rosewall Arena.
Kvitova had struggled with her breathing in her three-set win over Alexandra Dulgheru in the second round, a match played in the heat of the day.
Her asthma was much less a factor in the night match against the overpowered Hantuchova.
“It was not really bad tonight,” she said. “I have more problem in the USA than here. This is not really humid here.”