Playing in her first match of the tournament after receiving a first-round bye, Azarenka got past Michaella Krajicek 6-3, 7-5 and will meet wild-card entry Heather Watson.
Azarenka's season-opening streak, the longest on the WTA Tour in 15 years, has moved her to the top spot in the world rankings. She has won four tournaments this year, including the Australian Open, has lost just six sets and is the defending champion at this event.
Venus Williams, a wild-card entry, reached the third round by ousting No. 3 seed Petra Kvitova 6-4, 4-6, 6-0.
Williams will meet Aleksandra Wozniak, who got past Monica Niculescu 4-6, 6-3, 6-4.
No. 5 seed Agnieszka Radwanska advanced with a 6-1, 6-1 win over Madison Keys, but there were a host of surprises.
Garbine Muguruza Blanco, playing in the first tour event of her career, beat ninth-seeded Vera Zvonareva 6-4, 6-3; 11th-seeded Francesca Schiavone was ousted by Ksenia Pervak 6-4, 4-6, 7-5; and No. 18 Angelique Kerber lost to Zheng Jie 7-6 (7-4), 6-1.
Former world No. 1 Ana Ivanovic, seeded No. 15, was a 6-4, 7-5 winner over Vania King. Ivanovic reached the semifinals last week in Indian Wells, Calif.