Wozniacki and Kvitova, tuning up for next week's Australian Open, were on court for more than two hours in warm conditions after beginning their Australian campaigns indoors at last week's Hopman Cup in Perth.
Wozniacki was beaten by world number two Kvitova in three sets in the mixed teams Hopman Cup, after beating American Bethanie Mattek-Sands and Bulgaria's Tsvetana Pironkova in her other singles matches.
After her two hour and 22 minute match against the 18th-ranked Slovakian Dominika Cibulkova, the Danish world number one said her 7-5, 2-6, 6-4 victory had been a tough contest.
"I thought I didn't have that chance, but I never gave up the fight," said Wozniacki, whose tenure at the top of the women's singles rankings comes despite not yet winning a grand slam in 19 attempts.
"I'm happy to be through to the next round here. Definitely that I could fight back from that score is satisfying, but I definitely need to step up my game a little bit in the next round."
Wozniacki set up a quarter-final clash against Polish seventh seed Agnieszka Radwanska, who overcame Germany's Andrea Petkovic in straight sets. Wozniacki leads Radwanska 5-1.
On her much-anticipated contest with Kvitova for the top spot, the Dane said she was looking forward to it. Kvitova trails Wozniacki by 295 rankings points with 470 points up for grabs to the winner of the Sydney International.
"Petra is a great girl. I like her a lot. She's one of my good friends," she said. "I'm sure we'll play against each other and we'll both do well in the years to come", Wozniacki said.
"The most important thing is that we're all healthy and playing well. The competition on the court will be good fun for the fans as well."
Kvitova also a had tough fight against Romania's Alexandra Dulgheru, needing two hours and 18 minutes to defeat the world number 66 on the Ken Rosewall Arena.
The powerful left-hander, who became the third Czech woman to win Wimbledon last year, faltered in the heat during the middle set before regaining her form and setting up a quarter-final with Slovakia's Daniela Hantuchova.
"It's my first match in the tournament and the first outdoors," Kvitova said.
"I played four matches in Perth, but this is really different. I have to be playing in these conditions with the wind and sun. I need to play some outdoor matches before Melbourne.
"When I play outdoors it's the biggest problem for me. But today the serve was really good for me," she said.
Defending champion Li Na also had a difficult time before subduing South African Chanelle Scheepers 2-6, 6-4, 6-1 to set up a quarter-final with Lucie Safarova of the Czech Republic.
China's world number five Li had problems with Scheepers' power game before adjusting her tactics to take control.
"After the first set I changed a little bit to play the ball back more to the court and find a chance to win the point," said Li, who trained for four weeks in Munich in the off-season.
French Open semi-finalist Marion Bartoli skated into the quarters with a 6-0, 6-3 win over Australian Jelena Dokic and will play either third seed Victoria Azarenka or Jelena Jankovic of Serbia in the last eight.
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