She now faces Julia Goerges in the last eight after the German eighth seed claimed a 6-4 6-3 win over Elena Rodina of Russian Federation. Uncomfortable on the fastest surface, Osaka never looked like a decent opponent to the Kazakh who suffered three breaks of serve but destroyed the rival on the return, taking 60% of those points and seizing six breaks from ten chances.
The defeat of World No.1 Naomi Osaka at the hands of giantkiller Yulia Putintseva, also on Thursday, means that Barty could claim top spot in the world rankings for the first time in her career if she keeps winning in Birmingham and ends up lifting the Maud Watson Trophy on Sunday.
The Kazakh beat Osaka in their only previous meeting a year ago at the Hobart International - before the Japanese star went on to win the US Open and Australian Open titles - and maintained her mastery over the World No.1, sealing the upset after 68 minutes on Ann Jones Centre Court.
The 23-year-old Australian, fresh from her maiden grand slam triumph at the French Open, fired 11 aces and 24 winners to dispatch world No 51 Strycova in 84 minutes and stay in the hunt for her third title of the season.
Should Barty lift the title, she will usurp Australian Open champion Osaka and become only the 27th woman in 49 years to hold the No 1 ranking and head to Wimbledon as the top-seeded player.
"There are certainly times where tennis is on the back-burner and we are not thinking about it at all, so it is really important for me to be able to have that ability to switch on and off but then importantly on when I need to".
"I feel like I know exactly how I want to play in most matches, and it's just about going out there trying to execute as best I can".
"I'm happy with my level and happy with the way I played today". It's not easy to get to these quarter-finals.
Putintseva meanwhile recorded her fourth victory over a world number one, and she will face Julia Goerges in the next round.