The 18-year-old Wozniacki, from Denmark, smashed Croatian Karolina Sprem 6-1, 6-1.
Medina Garrigues, from Valencia, Spain, topped unseeded Julia Vakulenko of Ukraine 6-4, 6-4.
"I think I played a really good match," said Wozniacki, who qualified for a quarterfinal for the fourth time this season. "I played my game and I think we had quite a few long rallies. I'm happy I managed to pull it through. Karolina is a really good player so I'm happy I won the match today."
In other second-round matches, Petra Martic of Croatia downed former champion Klara Zakopalova of the Czech Republic 6-3, 4-6, 7-6 (7-3); while Russian Vera Dushevina trounced Englishwoman Katie O'Brien 6-3, 6-2.
The second round concludes on Thursday with top-seeded Maria Kirilenko of Russia facing Italian Roberta Vinci; and No. 2 seed Katarina Srebotnik of Slovenia plays German Julia Goerges.