The No 2-ranked Kvitova breezed through the first set of the quarter-final clash against the Slovakian but was tested in the second before serving it out 6-0 6-4 in just 63 minutes to book a place in the final four.
Kvitova, who will claim top-spot if she wins the tournament, will face defending champion Li Na in the semi-finals.
After cruising through the first set, China's world No 5 Li was forced to a tie-break by her Czech opponent Lucie Safarova in the second set but eventually wrapped up the quarter-final clash 6-2 7-6 (7-3).
"Of course I'm feeling good," Li said.
"I mean, I won in Sydney last year and this year I'm in the semis.
"It's just the beginning of the year, and I'm feeling much, much stronger."
World No. 3 Victoria Azarenka had a tightly-contested match with France's ninth-ranked Marion Bartoli but came out on top 7-5 6-4.