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Kerber came into the tournament in sensational form and gave home favourite Birrell little chance to settle.
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The German lost just a single game in the match, going on a nine-game winning streak to seal victory with a bagel, 6-1 6-0.
The 2016 champion will now meet American Danielle Collins in round four.
Kerber, who was celebrating her birthday on the day of the match, roared to the first set in just 27 minutes.
Her irresistible tennis hit a brief buffer when Birrell saved three match points at 5-0, but Kerber made no mistake with the fourth.