The top-seeded Azarenka of Belarus bested two-time Indian Wells champion Daniela Hantuchova in straight sets, 6-4, 6-1, in a 92-minute match.
She'll next meet 28th-seeded Belgian Kirsten Flipkens, who ousted Monica Niculescu of Romania 4-6, 6-4, 6-3.
Kerber, meanwhile, moved on with a 6-3, 6-2 win over Irina-Camelia Begu. Her next opponent will be Germany's Yanina Wickmayer, who rallied to best Croatian qualifier Mirjana Lucic-Baroni, 3-6, 6-3, 6-2.
The win earned her a berth in the round of 32 against Elena Vesnina of Russia, who came back to defeat Korean wild card Kimiko Date-Krumm, 3-6, 7-5, 6-1.
Other Saturday winners included seventh-seeded Australian Samantha Stosur, 11th-seeded Serb Ana Ivanovic, No. 24 Mona Barthel of Germany, China's Shuai Peng, 10th-seeded Russian Nadia Petrova and 21st-seeded German Julia Goerges.
Also notching wins Saturday were unranked American Jamie Hampton, Spanish qualifier Garbine Muguruza and Magdalena Rybarikova of Slovakia.