Top-seeded Simona Halep served for the match four times before prevailing 4-6, 6-4, 15-13 over American Lauren Davis in a marathon match at Rod Laver Arena.
Halep saved three match points in the 22nd game of the third set at 0-40 and Davis saved five break points in the 23rd game in the 3 hour, 45-minute match. The final set took 2 hour, 22 minutes and Halep won on her first match point when Davis hit a forehand wide along the sideline.
Davis twice had medical timeouts in the final set to have blisters on both feet treated.
Halep will play the winner of Saturday's later match between local hope Ashleigh Barty and Naomi Osaka.
In other women's third-round matches, sixth-seeded Karolina Pliskova beat Lucie Safarova 7-6 (6), 7-5 and No. 8 Caroline Garcia beat Lucie Safarova 6-3, 5-7, 6-2. Garcia will play Madison Keys in the fourth round.
