Lisicki became the first person to win a set off Williams at Wimbledon this year but still had to rally from an 0-3 deficit in the third set for a 6-2, 1-6, 6-4 win.
It was the first loss for Williams in a tournament since the second round in Dubai in February. She had won a personal best 34 consecutive matches from then until Monday.
Lisicki took the first set by winning the last four games. She also won the first game of the second set but Williams turned the match around quickly, winning nine consecutive games -- taking 14 straight points in one stretch -- for a second-set win and 3-0 lead in the third.
Lisicki broke back and the two traded breaks and then each held to 4-4 before Lisicki collected her fifth break of the day. She gave Williams one last break opportunity with a double fault but won the next three points to gain her second Grand Slam quarterfinal. She was a Wimbledon semifinalist in 2011.
Lisicki next goes against unseeded Kaia Kanepi, who topped Britain's Laura Robson in a tight 7-6 (8-6), 7-5 match.
Also in that half of the draw, fourth-seeded Agnieszka Radwanska came from behind for a 4-6, 6-3, 6-3 win over Tsvetana Pironkova. Radwanska, who lost her serve twice in the first set, only allowed Pironkova one break-point chance the rest of the way.
An impressive showing in the early session came from No. 6-seed Li Na, who routed 11th-seeded Roberta Vinci 6-2, 6-0 in 55 minutes. Li won nearly two-thirds of the points off Vinci's serve and finished off six of her seven break chances.
Radwanska and Li, two of the three Top 10 players remaining n the women's draw, are paired against each other in the quarterfinals.
Kvitova cashed in both of her break chances against Suarez Navarro and backed a solid service game by fighting off all but one of the break opportunities she faced.
No. 20-seed Kirsten Flipkens came away a 7-6 (7-2) winner over Flavia Pennetta behind six breaks. Flipkens, in her first Grand Slam quarterfinal, next plays Kvitova.