Petrova fell to Dominika Cibulkova 6-4, 3-6, 6-3 and Schiavone was an upset victim of Aleksandra Wozniak 6-2, 3-6, 6-2.
The tournament will feature top-seeded Venus Williams, who will play in the second round Wednesday in her first appearance since defeating her sister in the Wimbledon title match. Williams, one of three players to win Wimbledon and claim an Olympic gold medal in the same year, will try to repeat that achievement next month in Beijing.
Williams will meet Michelle Larcher de Brito in the second round.
Second-seeded Anna Chakvetadze, who also drew a bye past the first round, will face Shahar Peer Wednesday.