Kvitova, the winner in 2011, is the highest seed left in the bottom half of the draw and, with a game made for grass has emerged as a clear favourite to make the final.
But she has not had a good season and has been unconvincing so far this fortnight.
She may well have lost in the third round had bad light not intervened during her match against Ekaterina Makarova.
The eighth-seeded Czech looked better on Monday in a 7-6 (7/5) 6-3 win on Court Three against 19th seed Suarez Navarro, who is unusual among the top women in having a single-handed backhand.
It was still rather a struggle, with Kvitova securing the first break of serve in the 11th game only to be broken back to love, Suarez Navarro producing the shot of the match with a running backhand pass to set up the chance.
The tie-break was scrappy but Kvitova took it when the Spaniard netted a backhand.
Suarez Navarro, who was making a first appearance in the fourth round here, appeared to become distracted by noise from outside the court as she was broken again in the sixth game of the second set.
Kvitova survived two break points in the next game before clinching victory on her first match point when her opponent netted a forehand.