The eighth-seed dominated Anisimova's serve in the early match at Rod Laver Arena and smacked 18 winners to end the 17-year-old's fairytale run at Melbourne Park after less than an hour.
Lefthander Kvitova booked her first quarter-final appearance in Melbourne since her run to the 2012 semi-finals and first at a Grand Slam since the 2017 U.S. Open.
The Czech will meet either Maria Sharapova or Ashleigh Barty for a place in the semi-finals.
(Editing by Peter Rutherford)
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