The second-seeded Dane defeated her Dutch rival 6-4 6-3 in 86 minutes on Rod Laver Arena on Friday night.
Wozniacki threw her racquet in disgust after Bertens saved a match point - with replays subsequently showing Bertens to have hit a ball long earlier in the point.
Wozniacki won the next nine points, and 24 of the 31 points played from when she first faced match point.
Her win streak at Melbourne Park is now 11 straight matches after claiming the Australian Open girls' title in 2017 and coming through qualifying this year.
"I'm playing with house money". "I think it can be unsafe", she said. "I was like, Just try and stay aggressive".
Nadal, last year's runner-up, wasted no time in reaching the third round, dropping only one service game and making just 10 unforced errors in a 6-3, 6-4, 7-6 (7/4) win over Leonardo Mayer. Ostapenko, the seventh seed, will face No. 32 Anett Kontaveit on Thursday.
Fourteenth seeds Chan Hao-ching and Katarina Srebotnik faced a tougher time against Laura Robson of Britain and Coco Vandeweghe of the U.S., battling to a 7-6 (7/3), 6-4 victory in 1 hour, 36 minutes on Court 5.
With Sharapova and Kerber set to meet on Saturday evening, there is guaranteed to be at least one maiden grand slam finalist in next weekend's championship decider.
Ostapenko returned with her left thigh heavily bandaged and stole the momentum back from Kontaveit, roaring with delight as she took the second set in 34 minutes.
"Then I felt her tighten up just slightly".
She now plays another qualifier - big-serving Czech Denisa Allertova who romped past Magda Linette 6-1, 6-4 - for a place in the quarter-finals on Sunday.
But the story of the day belonged to 15-year old Ukrainian Marta Olehivna Kostyuk, who became the youngest woman to make it into the third round of a Grand Slam in over 20 years, after beating out home town hero Olivia Rogowska.
The second seed only scraped through to the third round by the skin of her teeth, saving two match points at 5-1 down in the third set against 119th ranked Jana Fett. "I think it was my experience today that made the difference".
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