The third-seeded Santangelo, from Italy, beat Russia's Alla Kudryavtseva, 6-2, 6-4. Mirza, from India, topped crowd favorite Tamarine Tanasugarn of Thailand, 6-4, 2-6, 6-1.
China's Shuai Peng overcame Italian Romina Oprandi, 6-7 (5-7), 6-1, 6-3; Austria's Sybille Bammer downed Russian Anastassia Rodionova, 6-2, 7-5; and Austria's Alicia Molik pulled out of the tournament due to a left hamstring injury.
Molik's decision to exit the draw means No. 6 seed Gisela Dulko of Argentina advanced to the quarters by a walk-over.
The second round will conclude Thursday, when one match will pit top-seeded Marion Bartoli of France and unseeded Martina Sucha of Slovakia.