Gauff announced her arrival last July with victory over her “idol” Williams, 39, in the Wimbledon first round.
And just like last time, she did it in straight sets, winning 7-6 (7-5) 6-3.
Gauff’s celebrations were slightly delayed because she did not realise the final point had been given her way.
“That was really difficult. She played really well and I was really nervous for today’s match – I was a bit shocked when I saw the draw, but glad I was able to get through it,” said Gauff, who was making her Australian Open debut.
“I am feeling great. I really like this court and really like this crowd.”
Gauff will play Romanian world number 74 Sorana Cirstea next.