Azarenka, the Belarusian defending champion at the BNP Paribas Open, rallied for a 3-6, 6-3, 6-0 victory over 28th-seeded Belgian Kirsten Flipkens in a 1-hour, 46-minute battle to reach the fourth round.
Also advancing Monday was No. 4 Angelique Kerber of Germany, who posted a 6-1, 7-6 (7-4) decision over 30th-seeded Yanina Wickmayer of Belgium.
Also Monday, eighth-seeded Dane Caroline Wozniacki downed No. 29 Elena Vesnina of Russia 6-2, 6-1; 10th-seeded Russian Nadia Petrova blasted 21st-seeded German Julia Goerges 6-1, 6-2; and 24th-seeded Mona Barthel of Germany got past No. 11 Serbian Ana Ivanovic 6-1, 3-6, 6-0.
Other winners included Spaniard Garbine Muguruza and Urszula Radwanska of Poland.