Kuznetsova swept past Nathalie Dechy 6-3, 6-1 in one of the most lop-sided women's matches of the second day of the year's first Grand Slam event.
But fourth-seeded Ana Ivanovic beat Sorana Cirstea 7-5, 6-3; eighth-seeded Venus Williams defeated Zi Yan 6-2, 7-5 and ninth-seeded Daniela Hantuchova handled Vania King 6-3, 7-5 in other straight-set decisions.
Sofia Arvidsson delivered the tournament's first Top-10 upset, knocking out 10th-ranked Marion Bartoli 6-7 (3-7), 6-4, 6-3. Other upset victims were 16th-seeded Dinara Safina, who dropped a 7-6 (7-4), 4-6, 6-2 match to Sabine Lisicki; 20th-seeded Agnes Szavay, who lost 3-6, 6-4, 7-5 to Ekaterina Makarova; and 22nd-seeded Lucie Safarova, who was ousted 6-1, 6-4 by Catalina Castano.
No. 6 Anna Chakvetadze advanced when Andrea Petkovic withdrew with a right knee injury only a couple of points into their match.
Fourteenth-seeded Nadia Petrova was a 6-1, 6-3 winner over Nicole Pratt and other seeded players to make it to the second round with Tuesday wins were No. 21 Alona Bondarenko, No. 24 Na Li, No. 27 Maria Kirilenko, No. 28 Katarina Srebotnik, No. 29 Agnieszka Radwanska and No. 31 Sania Mirza.