Taking to the court just before 11 p.m. local time, the pair slugged it out for two hours and 41 minutes in the late match at Rod Laver Arena before former U.S. Open finalist Pliskova finally put down her compatriot.
Strycova saved one match point with an audacious serve-volley and a second with an overhead smash before the 20th seed surrendered by clubbing a backhand over the baseline.
Pliskova will meet top seed Simona Halep for a place in the semi-finals.
"I think the first set was very close but I needed to step up and be more aggressive," the tall 25-year-old said in the on-court interview.
"I was playing fine the other two sets. On this surface I have a chance (against Halep)."
(Editing by Ed Osmond)
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