The 23-year-old, chasing her first grand slam title, will hope to improve on her last-16 appearance at last year's Wimbledon, when she lost to Latvia's Jelena Ostapenko.
"I was expecting a good match and she (Cornet) was producing some great rallies," Svitolina said.
"She plays well against the top players, she beat a couple of them in the past, and she really steps up her game. I'm very happy with the performance today."
Japan's Naomi Osaka was forced to retire due to an abdominal injury in her last-16 clash against Dalila Jakupovic, with the Slovenian qualifier leading 6-3.
"It's never nice to win when somebody's injured," the 27-year-old Jakupovic said. "I was trying to focus on my play, and I didn't really look on her side. I hope (Osaka's) going to be better for the next tournaments."
Jakupovic will next take on Slovakia's Magdalena Rybarikova, who mounted a comeback to win 3-6 6-2 6-1 against world number 56 Kristina Mladenovic.
Rybarikova, who reached the Wimbledon semi-finals last year, converted five break point opportunities and struck five aces in the encounter, which finished in just under two hours.
(Reporting by Anirban Paul in Bengaluru; Editing by Mark Heinrich)
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