Kerber defeated Alla Kudryavtseva 6-4, 4-6, 6-2 in one of three matches conducted Thursday that completed the second round.
No. 8 seed Ayumi Morita, who advanced Wednesday, will be Kerber's quarterfinal opponent.
The other two matches held Thursday saw third-seeded Maria Kirilenko fight off Jovana Jaksic 6-0, 4-6, 6-1 and Lauren Davis defeat Coco Vandeweghe 6-4, 7-6 (10-8).
Kirilenko will next meet Urszula Radwanska and Davis will take on Anastasia Pavlyuchenkova.