Kuznetsova, winner of the US and French Open titles, saw off her Spanish opponent 6-3 6-3 in an hour and 10 minutes.
Laura Robson beat the elements in the nick of time to get a first win since the Australian Open.
The British number two beat Camila Giorgi in three sets, seeing off the Italian 6-4 4-6 6-3, with match point cashed in as a thunderstorm started.
Simona Halep was also a winner on Wednesday but she was pushed to three sets before getting the better of Sabine Lisicki, the former Wimbledon semi-finalist, with a 6-2 3-6 7-5 triumph.
Also in the women's tournament, Daniela Hantuchova defeated Tsvetana Pironkova and there were successes for Jamie Hampton, Stefanie Voegele, Romina Oprandi and Melinda Czink.
In the men's event, Xavier Malisse, the world number 48, needed three sets to defeat Rajeev Ram, while Frenchman Michael Llodra was two-set victor over compatriot Benoit Paire.
Others to progress were Urszula Radwanska and Karolina Pliskova in the women's tournament, while in the men's event, Igor Sijsling went through, as did Grega Zemlja, while Lukas Rosol beat Gilles Muller and Tobias Kamke got the better of Blaz Kavcic.