It took Azarenka, seeded No. 2 this year, 72 minutes to claim the first set before she took a 7-6 (7-2), 6-2 decision over Johanna Larsson. Azarenka dropped her serve three times and had 23 unforced errors in the first set but didn't allow Larsson a break opportunity in the second set.
Third-seeded Maria Sharapova started fast before holding off Bethanie Mattek-Sands 6-3, 6-4. Sharapova won the first four games of the match before Mattek-Sands made the match more even.
It was hardly a clean win for Sharapova. She had nine double faults and 28 unforced errors but was also able to finish off half of her eight break chances. Two of those breaks came in the second set, including one in the ninth game that set up the win.
It was nearly midnight before Sharapova walked off the court Tuesday and temperatures were still in the 90s Fahrenheit. Temperatures reached 107 F degrees during the height of play Tuesday and the heat wasn't expected to break until at least the weekend.
Agnieszka Radwanska, the No. 5 seed, breezed through a 27-minute first set but needed nearly 2 hours after that to claim a 6-0, 5-7, 7-2 win over Yulia Putintseva.
Eighth-seeded Jelena Jankovic was on the court just more than an hour in beating Misaki Doi 6-1, 6-2. Jankovic had five breaks and took 60 percent of the points off Doi's serve.
No. 10-seeded Caroline Wozniacki raced past Lourdes Dominguez Lino 6-0, 6-2, winning about two-thirds of the points, while 11th-seeded Simona Halep took out Katarzyna Piter 6-0, 6-1 without dropping her serve. Those matches lasted a total of 2 hours, 1 minute.
Elina Svitolina took out 19th-seeded Svetlana Kuznetsova 6-3, 6-3 and Marina Erakovic edged by 21st-seeded Sorana Cirstea 6-4, 7-6 (8-6). Another upset saw Garbine Muguruza, who went through qualifying en route to winning last week's Hobart International, eliminating 24th-seeded Kaia Kanepi 6-2, 2-6, 6-2.