Li, who had advanced to the quarterfinals three times before at Wimbledon, looked out of sorts for most of the Court 1 match. She blew a set point in the second set.
Zahlavova Strycova called her win over Li the biggest of her career. Li won the first of her two Grand Slam titles at the French Open in 2011.
"When you go on court you have to believe in yourself," the 43rd-ranked Zahlavova Strycova said. "I thought I could do it, and I was pushing myself a lot."
The Czech player thought she had won the match and went to the net to shake Li's hand after a forehand was called out. But Li challenged the call and the ball was ruled in, continuing the match -- until Li double-faulted on match point.
"I was so happy already that the match is over, and then suddenly she took the challenge and I had to get back to my concentration," Zahlavova Strycova said.
Kvitova, the 2011 champion, broke Williams for the first time in the final game to close out the 2 hour, 30-minute match on Centre Court.
The left-handed Czech player had 11 aces and 48 winners. The 30th-seeded Williams had 29 winners.
Williams, winner of seven Grand Slam titles, had lost in the first round in her last appearance at Wimbledon in 2012.
Also, No. 4 seed Agnieszka Radwanska beat Michelle Larcher de Brito of Portugal 6-2, 6-0, while French Open finalist Simona Halep and former No. 1 Caroline Wozniacki were early winners under contrasting weather at the All England Club.
Midmorning rain that delayed play by about 30 minutes gave way to sunny skies by early afternoon. But there was a threat of additional rain and even thunderstorms as other matches progressed.
Halep, who lost the Roland Garros final to Maria Sharapova, advanced with a 6-3, 4-6, 6-4 win over Lesia Tsurenko of Ukraine in a second-round match. Wozniacki moved into the fourth round with a 6-3, 6-0 win over Ana Konjuh of Croatia.
It's the first time Halep has advanced past the second round in her fourth Wimbledon.
No. 22-seeded Ekaterina Makarova of Russia beat Caroline Garcia of France 7-5, 6-3, and Belinda Bencic of Switzerland defeated Victoria Duval of the United States 6-4, 7-5.
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