Wozniacki, seeking her maiden Grand Slam title, was upset by pocket rocket Cibulkova in her first match at the Sydney International, renewing questions about her durability as world number one.
But the 20-year-old always looked in charge on Friday and took advantage of some crucial Cibulkova errors to book a fourth round meeting with unseeded Latvian Anastasija Sevastova.
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While Cibulkova made 31 winners with her powerful groundstrokes she also made 41 unforced errors, many of those coming on key points.
The far steadier Wozniacki made only 11 winners, but she stayed in control because of her low error rate, just 11 over the two sets.
Wozniacki lost her serve twice in the first set but broke Cibulkova three times. It was a similar story in the second: Wozniacki was broken once but she broke Cibulkova twice to wrap up the match in 1hr 32min.
"Dominika is a tough player -- I lost to her in Sydney last week so I knew it would be a tough match," Wozniacki aid.
