After an error-strewn first set, the 26-year-old Gajdosova looked out of the match in the second when she rolled her left ankle on Rod Laver Arena and needed a medical timeout in the opening game.
The injury somehow sparked a comeback from Gajdosova, who exploited Kerber's weak service game, and local fans began to believe she might advance to the second round at Melbourne Park for the first time in nine attempts.
But Kerber, who lost in the Sydney International final to qualifier Tsvetana Pironkova on Friday, quickly forgot her second set troubles and raced through the decider in 31 minutes to set up a clash with Alla Kudryavtseva, who defeated France's Caroline Garcia 6-2 7-6(9).
(Reporting by Greg Stutchbury in Wellington; Editing by Peter Rutherford)
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