Konta found it hard to serve the match out - unable to claim victory when she had two match points at 5-2 in the final set, going on to lose the game.
Games went with serve in a blur, with few chances of a break until the seventh game when Kvitova saved two break points to stave off danger and hold for 4-3.
The eight-time Wimbledon champion lost only one point on his serve in the first set and didn't face a break point until he was up 3-0 in the third.
The British No 1, who weathered an early storm in a battle of fierce hitting from both players, was quick to extinguish fears she might be carrying an injury after calling for assistance after tumbling to the ground in the second set. Just happy I was able to keep a good perspective and just enjoy competing against her, because she's very tough to play on this surface.
Konta looked supremely confident, and no wonder given she had won 13 of her last 14 matches that had gone to a deciding set.
Roger Federer glided into the Wimbledon quarterfinals as he outclassed Italian youngster Matteo Berrettini, with the Swiss legend joining fellow tennis big guns Rafael Nadal and Novak Djokovic in the last eight.
"Obviously that's something I can be really proud of", she said. To know I have the capability to stay there as long as I need to - even if I lose the first set, I know I have every opportunity to get back into the match.
Konta had treatment on one of her feet during a change of ends but said it was nothing major. That's about it. There's levels when it comes to grand slam play, as the top tier players usually separate themselves from the rest of the pack and the players who are a few notches below struggle to sustain that level throughout the match.
Konta will undoubtedly be the favourite against 33-year-old Strycova, ranked 54, although the Czech did win their only previous meeting in Tokyo two years ago. "They were magnificent", she said of the Centre Court support for her. The ability to fight back has become a feature of her game this year. Halep, though, has experience of the latter stages at Wimbledon, reaching the semi-finals in 2014 and two quarter-finals since then. More than anything, I'm just pleased that I've been showing up every day.