Barty, ranked 223 in the world, scored a 7-5, 6-1 win over a player ranked 171 spots ahead of her.
"I've got goosebumps. This is amazing ... I'm shaking," the 20-year-old said.
In even better news for the Queenslander, she will face qualifier Mona Barthel for a spot in the round of 16 after the German beat Olympic gold medallist Monica Puig 6-4, 6-4.
Barty returned to tennis early last year after a stint playing professional cricket, with the Australian Open her first major campaign since the 2014 US Open.