Playing underneath the closed roof on Centre Court while rain halted play elsewhere at the All England Club, Williams hit 13 aces -- including three in the last game -- to beat the fourth-seeded Czech 6-3, 7-5.
Kvitova was on an 11-match winning streak at Wimbledon and had not lost here since Williams beat her in the 2010 semifinals en route to her fourth title.
"She's been playing so well on grass," Williams said. "I had absolutely nothing to lose."
The American four-time champion seized control by breaking Kvitova for a 4-2 lead in the first set and then never gave her opponent a chance to get back in the match. She saved a set point when trailing 5-4 in the second with a hard serve down the middle that Kvitova could return only into the net. That was the only break point the defending champion earned, as Williams won 86 percent of the points on her first serve.
Kvitova then led 30-0 in the next game but made four straight mistakes -- including netting an easy forehand on break point -- to give Williams the opening she needed.
Williams, who hit a Wimbledon-record 23 aces in a fourth-round win over Zheng Jie of China, is trying to become the first woman over 30 to win a Grand Slam title since Martina Navratilova won Wimbledon in 1990.
Outside Centre Court, it was a start-and-stop day at Wimbledon, as showers continued to cause headaches for organizers.
Play was delayed for about 30 minutes on the outside courts in the morning, although Andy Murray and Florian Mayer found enough time between the showers to wrap up suspended matches and reach the quarterfinals.
David Ferrer also advanced in the first match on Centre Court, where organizers again came under scrutiny for their use of the retractable roof. Their decision to open and then close it caused the start of Ferrer's match against Juan Martin del Potro to be delayed by about 40 minutes.
Murray made the last eight for the fifth straight year by beating the 16th-seeded Marin Cilic 7-5, 6-2, 6-3, while Mayer ousted Richard Gasquet of France 6-3, 6-1, 3-6, 6-2. American qualifier Brian Baker's remarkable run ended with a 6-1, 7-6 (4), 6-3 loss to 27th-seeded Philipp Kohlschreiber of Germany.
Rain had prevented five of the men's fourth-round matches from being completed on Monday. The weather continued to cause headaches as the start of play on outside courts was delayed for about 30 minutes because of light showers. When matches started, they were quickly halted again for another rain delay of about an hour.
"We stopped, obviously, a lot," Murray said. "You're always a little bit edgy when you come out after a rain delay when you have the momentum with you. You stop, and then you come back out, and it feels a bit like you start from scratch again. I needed to serve well today and I got a lot of free points that helped me out."
Play on Centre Court didn't even have time to start at all before the rain came. Organizers had closed the roof because of earlier showers in the morning but then decided to open it during a dry spell just before Ferrer's match against del Potro. When the showers resumed, they promptly had to close it again and keep the players waiting.
When the match began, Ferrer needed less than two hours to beat del Potro 6-3, 6-2, 6-3. Another rain delay then forced the suspension of Jo-Wilfried Tsonga's match against Mardy Fish, with the fifth-seeded Frenchman leading 4-6, 7-6 (4), 6-4, 4-2.
Murray's match was halted on Monday with the Briton leading 3-1, 40-0 in the second set. He had time to play one point on Court 1 -- clinching that game -- before rain started falling again. One game later, the match was suspended once more. After the second resumption, there was another slight break early in the third set as the players remained in their chairs for about five minutes under umbrellas as officials waited for a light shower to subside.
The Briton's victory never looked in doubt, though, and he served out the match to love when the Croat netted a backhand. Murray will next play Ferrer as he tries to become the first British man to win Wimbledon since 1936 -- a task that looks easier after Rafael Nadal was knocked out in the second round last week.
The 126th-ranked Baker was trying to become the third American qualifier to reach the quarterfinals at the All England Club. He was playing in Wimbledon's main draw for the first time after being off the tour for more than five years because of a series of operations, one on his right elbow. He was ranked 458th at the start of 2012 but now will rise inside the top 100.
On Monday, top-ranked Novak Djokovic, Roger Federer and Mikhail Youzhny were the only men to complete their round of 16 matches.
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