"I'm trying to stay aggressive," Wozniacki said in a court-side interview. "I still made some unforced errors. It's taking a few matches to play like 100 percent but I still felt I played pretty well today."
Top seed Wozniacki started brightly with a break of serve to love on her way to an early 3-0 lead and added another break in the eighth game to wrap up the opening set in just 24 minutes on a glorious day in New Zealand's largest city.
Martic tried to mount a comeback early in the second when she broke for a 2-0 lead but Wozniacki won the final six games behind impressive serving numbers, including six aces, to book a last eight encounter with young American Sofia Kenin.
"I've worked on everything I need to work on in the off-season," Wozniacki added as she continues her preparations for the Australian Open starting in Melbourne on Jan. 15.
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"Now it's just a matter of working out how to incorporate that into your match or into a situation where you maybe get nervous."
Kenin, a 19-year-old wild card, knocked out compatriot Varvara Lepchenko 6-4 7-6(6) earlier in the day and there were also victories for Taiwan's Hsieh Su-wei and Barbora Strycova.
Hsieh recorded a 6-4 6-3 triumph over Belgian qualifier Ysaline Bonaventure to set up a quarter-final clash against Strycova after the third seeded Czech edged out Sweden's Johanna Larsson 6-1 6-7(3) 6-2.
In the late matches, second seeded German Julia Goerges eased to a 6-4 6-0 victory over Slovakia's Viktoria Kuzmova to book a last eight tie against Slovenia's Polona Hercog, who was almost as ruthless in a 6-4 6-2 win over Kirsten Flipkens.
Former world number two Agnieszka Radwanska continued her strong start to the campaign with a 6-3 7-5 win over American Taylor Townsend, the Pole holding her nerve in a tight second set that lasted more than an hour to advance.
Fourth seed Radwanska, who remains on a collision course for a semi-final against Wozniacki, next faces American qualifier Sachia Vickery, who defeated Paraguay's Veronica Cepede Royg 6-2 6-4.
(Reporting by John O'Brien in Singapore; Editing by Greg Stutchbury/Amlan Chakraborty)
