Kuznetsova lost her serve three times but still claimed a 6-1, 7-5 win over Eleni Daniilidou. Kuznetsova had seven breaks over Daniilidou's 10 games serving. Daniilidou hindered herself with 14 double faults.
Third-seeded Petra Cetkovska won just seven more points overall while posting a 6-4, 6-2 decision over Melinda Czink. No. 5-seeded Simona Halep was ahead 6-1 when Fatima Zahrae El Allami, a local player, retired.
For the second night, a match was suspended due to darkness. Eighth-seeded Shahar Peer and Magdalena Rybarikova played more than 2 1/2 hours to a 5-7, 6-3, 5-5 tie. Rybarikova will serve when the match resumes.
The match that was suspended Monday, also 5-5 in the third, ended Tuesday with Arantxa Rus taking a 6-4, 5-7, 7-6 (11-9) win over seventh-seeded Klara Zakopalova.
Qualifiers Garbine Muguruza Blanco and Kiki Bertens earned spots in the second round. Muguruza Blanco got past Anna Tatishvili 7-5, 5-7, 6-4 in a match that took 2 hours, 40 minutes. Bertens topped Urszula Radwanska 6-4, 7-5, winning 53 percent of the points off Radwanska's serve.
Also moving into the second round Tuesday were Mathilde Johansson, who lost nine points -- three on double faults -- in beating Nadia Lalami 6-1, 6-1; Laura Pous-Tio, who had seven breaks in a 6-2, 6-1 rout of Olga Govortsova; and Timea Bacsinszky, who advanced when Anna Rodionova retired due to injury.