Suarez Navarro, the only seeded player on the schedule Tuesday, defeated Johanna Larsson 6-1, 6-4 in 68 minutes. Suarez Navarro was good on 85 percent of her first serves and ended up winning 69 percent of the points on serve.
She lost her serve just once while converting five of her nine break opportunities.
Hantuchova advanced when, after Hantuchova built a 6-3, 3-0 lead, Marina Erakovic retired. Hantuchova will next go against world No. 5 Maria Sharapova who is seeded No. 1.
Cornet draws second-seeded and sixth-ranked Petra Kvitova in the second round. Cornet was a 6-3, 5-7, 6-2 winner over Magdalena Rybarikova, cashing in all three of her break chances of the third set.