Zahlavova Strycova, the world number 43, had enjoyed the best win of her career in the previous round when she defeated Chinese second seed Li Na and she added Danish 16th seed Wozniacki to her list of upsets, converting a sixth match point to move into the last eight at a Grand Slam for the first time at the 32nd attempt.
The 28-year-old, who served a six-month ban for doping last year, will play compatriot Petra Kvitova for a place in the semi-finals.
"I didn't want to play again because I felt like it's a little bit unfair," she said.
"In the first two months, I didn't want to come back. It was tough, but on the other hand, it also brings me some positive things. I am seeing the sport a little bit different now. And here I am."
Sixth seed Kvitova, who won the Wimbledon title in 2011, routed world number 61 Peng Shuai of China 6-3, 6-2 in just one hour on Court Two.
Three of the four quarter-finalists in the bottom half of the draw are Czech after 23rd seed Lucie Safarova ended the fairytale run of teenager Tereza Smitkova, the lowest ranked woman left in the tournament, with a 6-0, 6-2 victory.
World number 175 Smitkova was attempting to become only the seventh qualifier to reach the quarter-finals, but the 19-year-old was thrashed by in just 47 minutes.
Safarova can look forward to her first Wimbledon quarter-final appearance, which will also be the 27-year-old's first last-eight clash at a Grand Slam since 2007.
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