The third seed produced six double faults and a string of errors before securing a last 16 clash with Russian Ekaterina Makarova, who upset 13th-seeded compatriot Nadia Petrova.
"You never play a whole tournament playing your best tennis. And you have to also, you know, work for it. I think that's what I had to do today," the Belgian told the official Australian Open website.
"Just little things that keep that rhythm or get the rhythm to where I want it to be."
Third-seeded Clijsters came into the first grand slam of 2011 as one of the favorites having retained her U.S Open title last year, but after a strong start in which she took a 3-1 lead in the opening set, errors starting to creep in.
Cornet broke back to level only for Clijsters to claim her second break to pull again at 5-4 and serve for the set.
But she was broken again after a forehand volley error left Cornet with an opportunity she seized.
The first set tiebreak, which Clijsters took 7-3, proved decisive as Cornet also made unforced mistakes.
A single break in the fourth game of the second set was enough for Clijsters to seal victory against Cornet, who put up a fine show on her 21st birthday.
Well, I knew this was gonna happen, she's been playing so well that it was only a matter of time before she had a bad match (42 unforced errors ouch!).
The good news is that despite Clijsters not playing her best her opponent had nothing to hurt her with so Kim made it through.
There was a moment there when I thought the match would turn into the disappointment that was last year (with Kim exiting in the 3rd round courtesy of a thrashing from Nadia Petrova).
That really was a heart breaker because Kim completely fell apart right from the get go, and couldn't get herself together enough to even put up a fight.
In this one she started off well, and went off the rails at certain points the difference this time being she kept her cool and pulled it out in straight sets.
Had Petrova won there would have been a re-match of last year's nightmare.
Thankfully Ekaterina Makarova pulled off an upset so that won't happen.
Since I don't know much about this player I won't make any predictions, but I'm sure Kim will regroup and play better then this match (or at least I hope so).
Otherwise I won't have a reason to watch the women's matches.