US Open champion Naomi Osaka came back from within two games of an Australian Open third-round exit to beat Taiwanese Hsieh Su-wei 5-7 6-4 6-1.
Sixth seed Elina Svitolina also diced with danger in a 4-6 6-4 7-5 win over Chinese world number 40 Zhang Shuai.
Japanese fourth seed Osaka lost the first set and was a break down in the second.
But she broke back twice at the end of the second and won seven games in a row to take the advantage in the decider.
The 21-year-old will face China's 21st seed Wang Qiang or Latvian 13th seed Anastasija Sevastova in the next round.