Zhang arrived in Melbourne having lost 14 consecutive first round matches at major tournaments.
She broke down in tears after ending that run with a stunning win over world number two Simona Halep on Tuesday and then followed it up with another victory, beating world number 33 Cornet 6-3 6-3.
Zhang, ranked 133rd in the world, will now face American Varvara Lepchenko in round three and she is eager for her Melbourne fairytale to continue.
“(It’s) Like a dream come true,” Zhang said.
“But I’m looking forward (to the) next match, yeah. I don’t want stop right now. I want to keep winning.
Zhang was a deserving winner on Court 2 as she broke Cornet’s serve five times in the match and hit 18 winners to the Frenchwoman’s seven.
“I lost 14 times (in the) first round. Maybe because (it was) 14 times, (it) gave me a lot more energy to work hard,” Zhang said. “I’ve won five matches already. I want to (say) thanks for last 14 times, yeah.”
Elsewhere, Ana Ivanovic was left badly shaken when an elderly spectator fell on a flight of stairs during her third-round match, delaying play for almost 30 minutes as she received medical treatment.
The Serbian 20th seed, who eventually beat Latvian qualifier Anastasija Sevastova 6-3, 6-3, said she froze when the sound of the spectator’s fall rang through Rod Laver Arena.
“Actually it was — well, first I felt really bad. I was really shaking, because the sound of the lady falling was really loud. I could hear it,” she said of the incident at 4-3 in the first set.
“I stopped immediately. It was really unfortunate, but, I mean, it was the same for both of us.”
Also into the third round of a grand slam for the first time is Japan’s Naomi Osaka, who upset the odds to knock out 18th seed Elina Svitolina.
The 18-year-old Osaka is one of the most exciting talents on the tour and she will now go up against 14th seed Victoria Azarenka.
“I just wanted to qualify. That’s all I was expecting,” Osaka said. “I never feel pressure from playing someone that’s supposed to be like better than me. I’m just going to go in there happy and hopefully try to pull off an upset.”
Third seed Garbine Muguruza is also through, along with seventh seed Angelique Kerber and 15th seed Madison Keys.
Jelena Jankovic of Serbia, however, is out. The former world number one lost in three sets to Germany’s Laura Siegemund.