Serving for the match at 5-3 under the lights of Rod Laver Arena, the former world number one harangued the chair umpire when a line call went against her and pounded her racquet into the blue hardcourt when Bertens saved a second match point.
Bertens, seeded 30th, cancelled out a third match point with a ripping return down the line but Wozniacki sealed the fourth with a huge serve that the Dutchwoman could only fire long.
In her previous match, Wozniacki had to save two match points on an epic comeback from 5-1 down in the third set against Croatian Jana Fett, so she was thrilled to avoid another drawn-out battle against Bertens.
"Right now I'm playing with house money," the Dane, a semi-finalist at Melbourne Park in 2011, said in her post-match interview on court.
"Right now I've got nothing to lose ... I got a second chance and I'm going to try to take it and see how far I can go."
Wozniacki will meet Slovakian 19th seed Magdalena Rybarikova for a place in the quarter-finals.
(Editing by Toby Davis)
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