Sharapova looked to be showing no ill-effects of her near three-and-a-half-hour epic against Karin Knapp in baking hot temperatures last time out, as she took the first set against her French opponent inside 32 minutes in much cooler weather in Melbourne on Saturday.
But the Russian visibly wilted as the match went on, wasting two opportunities to serve out for the match, and appeared to be running on empty before eventually coming through 6-1 7-6 (8/6).
The 2008 champion barely broke sweat in racing into a 4-0 first-set lead, with Cornet's tentative approach playing straight into Sharapova's hands.
Cornet fired a forehand long to go a break down and there would be no let up as she found herself 15-40 behind in her next service game, with Sharapova clinically sealing the double break.
Cornet did get on the scoreboard, but the 23-year-old then dropped her own serve to love before third seed Sharapova wrapped up the first set in 32 minutes.
Cornet buried her face in her towel at the change of ends and came out firing at the beginning of the second set, fighting back from 0-40 down in the third game to hold serve after several uncharacteristic errors from Sharapova.
She made Sharapova pay for her lapse by going a break up with a lovely backhand half-volley at the net, but she could not consolidate and lost the next three games.
Sharapova first broke to love and in Cornet's next service game, two excellent forehand winners put the four-time grand slam champion in control.
The 26-year-old could not convert her first match point on Cornet's serve and then failed to serve it out, to the delight of the Rod Laver Arena crowd.
Sharapova sealed yet another break with some positive intent but once again, she could not hold her own serve and the chance to seal victory went begging.
The tiebreak followed the pattern of the second set, with the players exchanging several mini-breaks, but it was Cornet who had the first opportunity at 6/5 ahead, only for Sharapova to level proceedings.
Cornet then put two successive forehands long as Sharapova eventually got over the line.