The Dane trailed Croatian world number 119 Jana Fett 1-5, 15-40 in the deciding set before saving two match points and then winning six games in a row.

She eventually triumphed 3-6, 6-2, 7-5 in a match lasting 2 hours 31min.

Wozniacki credited her "competitive" family afterwards which includes her mother, Anna, who played volleyball for Poland.

Father Piotr was a professional footballer.

"If you lose a game to anyone in my family, you're going to hear about it for at least a week," the 27-year-old said.

"That definitely helped me.

"Growing up, I never wanted to lose, and the worst was to lose to my brother. 

"Giving him the opportunity to be ahead was not pleasurable. 

"So I think from that point, you just learn and fight."

Ukrainian 15-year-old Marta Kostyuk beat Olivia Rogowska of Australia elsewhere today 6-3, 7-5 to become the youngest player in more than 20 years to reach the third round.

Rafael Nadal withstood a spirited performance from Leonardo Mayer of Argentina to progress in the men's draw.

The world number one prevailed 6-3, 6-4, 7-6.

"It's an important victory for me, a tough opponent," the Spaniard said.

"Leonardo is a player with big potential, he hits the ball so strong."

Third seed Grigor Dimitrov also survived an epic duel before defeating American qualifier Mackenzie McDonald.

The Bulgarian won 4-6, 6-2, 6-4, 0-6, 8-6.