Cornet admitted the win was especially sweet considering Williams had dominated her in the past.
"We have played many times and I was losing in straight sets. Now I can beat her in Hong Kong!" said Cornet, who faces Serbian Jelena Jankovic in the next round. "It means I used a good tactic, I played a very good match, and I believed in it."
Williams wasn't the only one to make an abrupt exit as third-seeded Brit Johanna Konta withdrew from the tournament with an abdominal strain. Konta's withdrawal could put her chances of qualifying for the season-ending WTA Finals in jeopardy as she resides in the eighth and final spot in the standings with several players in contention.
Top-ranked Angelique Kerber of Germany wasted little time finishing off her rain-delayed second-round match against American Louisa Chirico, winning four of the final five points on Thursday.
In other matches, fifth-seeded Denmark native Caroline Wozniacki breezed to a 6-3, 6-3 victory over Great Britain's Heather Watson and eighth-seeded Australian Daria Gavrilova posted a 6-2, 7-5 triumph over Czech Katerina Siniakova.
Sixth-seeded Frenchwoman Caroline Garcia was not as fortunate, dropping a 4-6, 6-2, 6-2 decision to American Bethanie Mattek-Sands.
Defending champion Agnieszka Radwanska of Poland withdrew from the tournament with a right thigh injury shortly after posting a 6-1, 6-1 victory over Russian Evgeniya Rodina to reach the quarterfinals in China.
"It's the end of the season, I guess everyone is struggling with something," Radwanska said in comments on the WTA website.
Radwanska's withdrawal allowed China's Peng Shuai to advance to the semifinals. Shuai breezed past Taiwan's Kai-Chen Chang 6-3, 6-2, in her quarterfinal match.
Olympic gold medalist Monica Puig of Puerto Rico cruised to a 6-4, 6-2 win over Spaniard Lara Arruabarrena and American Alison Riske advanced with a 6-3, 7-6 win over Poland's Magda Linette.
Generali Ladies Linz
Third-seeded American Madison Keys didn't face much of a test against Japan's Misaki Doi, breezing to a 6-2, 6-0 victory to advance to the quarterfinals in Austria.
Keys recorded five aces to advance to play French qualifier Oceane Dodin.
Defending champion Anastasia Pavlyuchenkova of Russia overcame a sluggish start to post a 6-4, 7-6 (2) triumph over Belgium's Kirsten Flipkens.