Venus will meet American Sloane Stephens in the semi-finals after she beat Latvian Anastasija Sevastova in another three sets 6-3, 3-6, 7-6 (7/4).
"I'm glad that I am still able to compete on the high level against the top players," said Kvitova after the match against Venus.
"I'm not sure about the titles of the Grand Slams. Of course, that's why I'm playing tennis, and that's why I wanted to be back and playing and is a big motivation."
"But I'm still on the earth, and I know it's still a lot of work. This was a quarter-final, but I know how tough it is to get a title for a Grand Slam. It was pretty close but pretty far, as well," Kvitova added.
American Venus Williams, 37, overcame Czech Republic's Petra Kvitova to become the oldest Grand Slam semi-finalist in the open era.||Venus will meet American Sloane Stephens in the semi-finals