American star Williams, a 13-time Grand Slam winner, needed three sets to defeat Yaroslava Shvedova and Kvitova, of the Czech Republic, beat Italian Francesca Schiavone.
The two winners will clash in the quarterfinals.
Big-serving German Sabine Lisicki, the 15th seed, eliminated Sharapova, avenging her semifinal loss to the Russian at Wimbledon last year.
Belgian Kim Clijsters, unseeded and playing in her last Wimbledon, was whipped by German Angelique Kerber 6-1, 6-1. Clijsters, a four-time Grand Slam winner, plans to retire after the U.S. Open this fall.
Conditions at Wimbledon were cold and rainy, delaying some matches.
Williams sailed through the first set, then had a fight on her hands before escaping with a 6-1, 2-6, 7-5 victory over Shvedova from Kazakhstan.
Kvitova outlasted Schiavone 4-6, 7-5, 6-1.
Lisicki knocked Sharapova out of the tournament in 84 minutes, slamming six aces and breaking the veteran star four times.
Sharapova, who won the Wimbledon title in 2004, completed a career Grand Slam last month by winning the French Open title.
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LAUSANNE, Switzerland, June 18 (UPI) --A new computer algorithm that can give humans the ability to map their environments with sound could lead to an app to aid blind people, Swiss researchers say.