Denmark's Wozniacki trailed Slovakia's Dominika Cibulkova 4-0 in the third set of their second round encounter in the Ken Rosewall Arena before the top seed eked out a 7-5 2-6 6-4 victory in the final warm-up event for the Australian Open.
"I hate losing," Wozniacki said bluntly afterwards. "That's what I put it down to. I just hate to lose. I always do everything I can to win a game. I want to stand in the end as the winner having won the last point."
Kvitova, an asthma sufferer, appeared fatigued and breathless in the stifling conditions but held on for a 7-5 3-6 6-4 win against Romania's world number 66 Alexandra Dulgheru.
"It's my first match of the tournament and my first match outdoors this year," Kvitova said.
"I have to get used to these conditions with the wind and the sun. I still have a long way to go. I lost to Alexandra at the US Open and that was a little bit in my head. I really need these matches before Melbourne. I know that I played four matches at the (team event) Hopman Cup in Perth, but it wasn't really a tournament.
"I need to play some outdoor matches before Melbourne. The sun and the wind are the toughest conditions for me."
Kvitova next meets Slovakia's Daniela Hantuchova after the world number 21 downed Italian world number 11 Francesca Schiavone 7-5 6-1.
Wozniacki pounced in her match when world number 18 Cibulkova was struck by nerves with the finishing line in sight at 4-0.
"I thought I didn't have a chance, but I never gave up," she said. "I just tried to hang in there. It paid off today and I'm pretty happy about that. I was in my own little bubble and I just kept going. I didn't really play well and she was hammering the ball. I was just standing there and trying to figure out what to do.
"I felt like everything I tried to do wasn't working and I was making a lot of unforced errors. So I said OK, let's just keep the margin for error down and give her that extra ball.
"It paid off in the end. I could feel she got a little bit nervous. Coming back from that score is definitely satisfying but I need to step it up in my next round."
World number five Li Na was another big name to survive a scare, recovering from a slow start to eclipse South African Chanelle Scheepers 2-6 6-4 6-1.
Also through to the quarter-finals is Marion Bartoli after the Frenchwoman's 6-0 6-3 defeat of Australian Jelena Dokic.
Wozniacki predicted the current rankings battle was only the start of a long rivalry with Kvitova.
"Petra is a great girl," she said. "I like her a lot. She's one of my good friends. I'm sure we'll play against each other a lot in the years to come and we'll both do well. The most important thing is we're all healthy and playing well. The competition on the court is going to be great for the fans."