Top-seed Wozniacki, who is looking for back-to-back titles having won the BNP Paribas Open last week in Indian Wells defeated American Bathanie Mattek-Sands, ranked 42 in the world 6-2, 7-5.
Although it was a straight-sets victory, Wozniacki at times struggled with her game, hitting only 5 winners but crucially saved 8 of 10 break points.
Former world number one Maria Sharapova will be hoping to continue with the form that saw her reach the semi-finals last week in Indian Wells. The Russian player eased past wildcard Petra Martic of Croatia for the loss of just 5 games, 6-2, 6-3.
The first shock of the tournament saw Israel's Shahar Peer, seeded 10 lose to Anabel Medina Garrigues 6-2, 6-2.
Britain's Elena Baltacha is out of the tournament after losing 7-6 (7-4) 6-3 to 32-seed Klara Zakopalova.
The 27-year-old British number one put in a good performance but found her opponent too much on the day and lost in an hour and 27 minutes.
