Kuznetsova, who titled at Crandon Park in 2006, breezed past Spaniard Lourdes Dominguez Lino 6-3, 6-3 on Day 2 of the women's singles draw.
She was joined in the second round by American Jamie Hampton, who had little trouble with Romanian Monica Niculescu in a 6-4, 6-3 triumph.
Poland's Urszula Radwanska, Switzerland's Romina Oprandi and Stefanie Voegele, Spaniard Garbine Muguruza and Belarus' Olga Govortsova each collected a Wednesday victory as well.
Disney's 'Jessie' to feature network's first engagement
Chipotle plans first price increase in 3 years