Playing her second-round match before a frenzied home crowd, Mirza beat unseeded Sandra Kloesel of Germany, 7-5, 6-3.
"I'm taking it one match at a time," Mirza said. "I'm really happy to be here in the quarterfinals in front of a great crowd. I was glad to get out with a win in two sets."
In other matches, unseeded Olga Poutchkova of Russia topped No. 7 seed Nicole Pratt of Australia, 6-2, 2-6, 6-2; Alberta Brianti of Italy beat Angelique Widjaja of Indonesia, 7-6 (9-7), 3-6, 6-3; unseeded Alla Kudryavtseva of Russia downed Hana Sromova of the Czech Republic, 6-2, 6-0; and Iroda Tulyaganova of Uzbekistan trounced Casey Dellacqua of Australia, 6-3, 6-2.
Iranian woman stops the execution of son's killer
Rosie O'Donnell unveils nearly 50-pound weight loss