The last time either player reached a quarterfinal, they squared off with each other earlier this summer at Wimbledon. Kvitova ended Zahlavova Strycova's best Grand Slam run and went on to capture her second title at the All-England Club.
Kvitova was the only seed to make the last eight in New Haven, where she won the title in 2012 and was runner-up in 2013.
The Turning Point
Zahlavova Strycova got up an early break and eventually took a 4-2 first set lead, but Kvitova found her form and won four straight games to take the first set.
Then from 1-1 in the second set, Kvitova really caught fire, not surrendering another game and winning the last 12 points of her 6-4, 6-1 victory.
By The Numbers
Kvitova dropped just seven points on her first serve, won all but four points on her opponent's second serve and converted on four of five break points.
All of that added up to Kvitova improving to 5-1 against Zahlavova Strycova and to securing her 10th win in her last 11 matches here.
"I was not really sure I could play a lot of rallies with her because I know she's a very good mover," Kvitova said. "I knew it wouldn't be easy and that I had to be really prepared physically and mentally. I wasn't ready from the beginning, but then I got more comfortable on the court.
"I'm glad to be back. It's just beautiful here. We have a great hotel close to the site. Center court is beautiful. Lots of people come to watch us. I really can't wish for anything more."