Temperatures again climbed well past 100 degrees Fahrenheit during the day session. Even after 10 p.m., when several matches were still on the court, temperatures were in the mid 80s.
The extreme heat caused a suspension of play in the afternoon and some evening matches were stopped because of rain, pushing play past midnight on the women's side.
The heat was expected to continue Friday before a sharp drop to highs in the upper 60s Saturday
Sharapova battled through 12 double faults and 67 unforced errors before escaping Karin Knapp's challenge with a 6-3, 4-6, 10-8 win in 3 hours, 28 minutes in 107 degree F. conditions.
Sharapova twice took leads in the third set, with Knapp saving three match points to get to 5-5. But Sharapova picked up break No. 7 on the day for a 9-8 lead and, after fighting off a break point, finished off the win.
Victoria Azarenka, the No. 2 seed and two-time defending champion, raced to an early lead en route to a 6-1, 6-4 win over Barbora Zahlavova Strycova with the second set taking nearly an hour. Azarenka won 53 percent of the points off Zahlavova Strycova's serve.
No. 10-seeded Caroline Wozniacki overcame a down second set for a 6-0, 1-6, 6-2 win over Christina McHale and 11th-seeded Simona Halep won two-thirds of the points in the second and third sets of a 4-6, 6-0, 6-1 win over Varvara Lepchenko.
Sloane Stephens, seeded 13th, lost a large third-set lead before prevailing 3-6, 6-2, 7-5 over Ajla Tomljanovic and No. 16-seeded Carla Suarez Navarro got by Galina Voskoboeva 7-6 (7-2), 3-6, 8-6 with the third set taking 1 hour, 21 minutes.
Kurumi Nara and Yvonne Meusburger posted small upsets. Nara took out 32nd-seeded Magdalena Rybarikova 6-4, 6-3 and Meusburger was a 3-6, 6-3, 6-2 winner over No. 33-seeded Bojana Jovanovski in a match that ended past midnight.
Other seeded players gaining places in the third round were 20th-seeded Dominika Cibulkova, No. 25 Alize Cornet and 29th-seeded Anastasia Pavlyuchenkova. Additional unseeded winners Thursday, as the second round was completed, included Elina Svitolina, Garbine Muguruza and Zarina Diyas.