Top-seeded Kvitova lost her first set to American Varvara Lepchenko but dropped only three games the rest of the way in the 4-6, 6-2, 6-1 win.
No. 2 seed Wozniacki went down one set to German Sabine Lisicki before bouncing back for the 3-6, 6-2, 6-3 triumph.
"I probably didn't play as well as I would want in the first set. But she started very strong and didn't give me time to do anything, so I was under pressure a little bit," Kvitova told reporters. "In the second set, I had to change the game a little bit and when I made the first break in the sixth game I was feeling a little better, more confident and I was just trying to keep going and not have so many unforced errors."
Wozniacki battled an illness throughout her match.
"I felt nausea during my match," Wozniacki told wtatennis.com. "I just feel pretty tired probably from coming from Hong Kong. I played pretty well today but maybe my movement wasn't quite there. I just hope I feel better for tomorrow."
Third-seeded Kiki Bertens breezed into the quarterfinals with a 6-3, 6-1 win over Anna Karolina Schmiedlova.
No. 4 seed Carolina Garcia was not as fortunate. The Frenchwoman fell to Germany's Andrea Petkovic 6-1, 6-1.