The two met in the US Open third round last September, with Naomi prevailing and having to console the 15 year-old, who had broken into tears.
To beat Cirstea, Coco rallied after losing the first set and got the pivotal service break in the next-to-last game before serving out against 29-year-old Cirstea, who is playing at the Australian Open for a 12th time.
Gauff started the tournament with her second first-round win over Venus Williams in three majors, following her upset over the seven-time Grand Slam champion at last year’s Wimbledon.
Osaka had to overcame swirling winds on Margaret Court Arena to beat Zheng Saisai 6-2, 6-4 in one of the first matches on Day 3.
Gauff reached the fourth round on her Wimbledon debut and the third round at the U.S. Open.
The 15-year-old is the youngest player in the tournament but she showed the fighting spirit to secure a 4-6, 6-3, 7-5 win.
Even in the final set Gauff had to face adversity as she trailed 3-0 early on.
Melbourne Arena was heavily backing the American with chants of her name in between almost every point.
And the teenager claimed that is what spurred her on to set-up a mouthwatering third-round clash with Naomi Osaka.