The No. 7 seed levelled in the eleventh game to send it to a tie-break - which the No.22 seed Sakkari sealed.
But Kvitova bounced back with an immediate break in the first game of the second set before doing so another three times to take it 6-3.
And the third was a more straightforward affair for Kvitova, who had not dropped a set in the tournament up until Sunday's clash, as she brushed aside her Greek opponent with some aggressive play from the baseline.
Kvitova will play either home favourite Ash Barty or American Alison Riske in the quarter-finals.
Australian Open : Sakkari flossing in front of the security camera!
Kvitova: My serving helped
“It’s tough playing Maria, I lost to her last time [in Cincinnati last year], so I knew it was going to be a difficult match.
"I was down a break in the first and make it to tie-break and I lost it so obviously I knew I had to fight hard.
Kvitova: I'm still questioning myself how the match changed
“Eventually I got used to her game a bit. I was playing more rallies and find my game but not much risk and my serving generally helped.
“To be honest I don’t have a problem finding the motivation [to keep competing].
My motivation is to play tennis on huge courts such as the Rod Laver Arena.