The Russian second seed eased through 7-5 7-5 against American Christina McHale, while fourth seed Petra Kvitova also went through with a 7-5 6-4 victory over Anastasia Pavlyuchenkova.
Serena Williams is in action against Galina Voskoboeva in the late match on Tuesday.
Those were second-round clashes, with most other matches on day two in the opening round.
Seeds to fall were Sabine Lisicki of Germany, Jelena Jankovic of Serbia and Maria Kirilenko of Russia; they were beaten by Romania’s Sorana Cirstea, New Zealand’s Marina Erakovic and Italy’s Flavia Pennetta respectively.
Venus Williams is unseeded but beat beat Simona Halep of Romania 6-3 6-4, while 14th seed Dominika Cibulkova of Slovakia beat Mirjana Lucic of Croatia 6-1 6-2.
Karin Knapp (Italy) beat Roberta Vinci (Italy) 6-4 2-6 6-2
Sara Errani (Italy) beat Timea Bacsinszky (Switzerland) 6-0 3-0 (retired)
Nadia Petrova (Russia) beat Andrea Hlavackova (Czech Republic) 6-3 6-3
Sloane Stephens (US) beat Anna Chakvetadze (Russia) 6-2 2-6 6-4
Silvia Soler Espinosa (Spain) beat Alberta Brianti (Italy) 6-2 6-1
Petra Cetkovska (Czech Republic) beat Olga Govortsova (Belarus) 7-5 6-4