Kvitova took down Errani 6-4, 6-4 in just under two hours to secure a spot in the semifinals.
The 21-year-old Kvitova, the No. 2 seed, rallied from a 4-1 deficit in the second set to become the first Czech woman to reach the semifinals at the Australian Open since Jana Novotna in 1991.
Kvitova beat Maria Sharapova in last year's Wimbledon finale and is also the reigning WTA Championships titlist.
The 24-year-old Errani was playing in her first-ever major quarterfinal.