Sharapova, who won the title in 2006 and lost to top-seeded Victoria Azarenka in last year's fiinal, was perfect 6-for-6 on break point against No. 47 Francesca Schiavone of Italy and wrapped up the 6-2, 6-1 victory when Schiavone double faulted.
A few minutes earlier, Kuznetsova had gotten her third service break of the match to finish off an 0-6, 6-2, 7-5 win over former No. 1 Jelena Jankovic of Serbia, the 18th seed.
Kuznetsova, a one-time No. 2 who missed much of last year with a right knee injury, got to match point on Jankovic's serve with an inside out forehand and closed out the match with a forehand down the line.
Sharapova will face No. 25 seed Carla Suarez Navarro of Spain in the third round and Kuznetsova will face No. 9 seed Marion Bartoli of France, a 6-3, 6-3 winner over South African Chanelle Scheepers.
Petra Kvitova, Maria Kirilenko, Sara Errani, Roberta Vinci, Dominika Cibulkova, Sorana Cristea, Johanna Larsson and qualifier Lesia Tsurenko also moved into the third round of the women's draw.
Meanwhile, the men's first round continued with American veteran James Blake overpowering Robin Haase of The Netherlands, 6-3, 6-4 to set up
Pablo Andujar of Spain outlasted Steve Johnson, a two-time NCAA champion at the University of Southern California, 2-6, 6-1, 6-4; Ivo Karlovic of Croatia served 12 aces in a 3-6, 7-6 (8), 6-2 win over Jack Sock of the U.S.; Nikolay Davydenko of Russia beat Paul-Henri Mathieu of France, 7-6 (1), 6-2; and Albert Ramos of Spain posted a 6-3, 6-3 win over Horacio Zeballos of Argentina, who recently beat Rafael Nadal in the final of a clay court event in Chile.
Nadal (5), Roger Federer (2) and David Ferrer (4) are among the seeds who will be in action when the men's second round begins Saturday.