The warm-up tournament’s top seed, who is back on tour for the first time since the US Open following mental health struggles, will face either Petra Martic or Maryna Zanevska after defeating Cornet 6-4 3-6 6-3 over two hours and two minutes.
“I really love playing here,” Osaka said in comments shared on the WTA after the match.
“I love New York, but this might be my favourite slam so it feels really good to always come back here.”
The Japanese player committed 57 unforced errors, including eight double faults, as she struggled with her accuracy at Melbourne Park.
Osaka took the opening set and took an early break in the second before Cornet fought back to win four straight games and the set.
The former world number one, now ranked 13th, claimed the first three games of the final set then served out the win from a 0-30 deficit.
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