The sixth-seeded Stosur, who won last year’s US Open title and reached the final at Roland Garros in 2010, beat Elena Baltacha of Britain 6-4, 6-0 in the first match on the tournament’s main court.
Kuznetsova won the French Open title in 2009 and the US Open in 2004 but is seeded No. 26 this year. Against Mirjana Lucic of Croatia, the Russian faced little trouble despite being broken twice in the second set. No. 10 Angelique Kerber of Germany and No. 20 Lucie Safarova of the Czech Republic also advanced to the second round, along with American players Melanie Oudin and Irina Falconi.