On paper the 6-2, 7-6 win looked comfortable enough but it was far from straightforward as Rybakina's power game malfunctioned badly after she had looked on course for a quick finish.
The Moscow-born Kazakh slammed winners all over Centre Court in a one-sided opening set and appeared to be racing towards victory against her opponent.
But Rybakina's game went from red hot to decidedly lukewarm as the wily Cornet, playing in her 66th successive Grand Slam tournament, used her experience to dig in.
As the errors flowed off Rybakina's racket she was locked in a tense game at 5-5 in which Cornet had five break points before slipping awkwardly on the baseline and needing lengthy treatment before eventually carrying on.
Rybakina then held serve on her 10th game point but was still looking edgy as she was dragged into a tiebreak.
Eventually the third seed got the job done but it was far from convincing in the end.
She will next face wildcard Katie Boulter (26), Britain's last remaining player in the women's draw.