Wozniacki, the WTA International tournament’s top seed, cruised past Germany’s Julia Goerges 6-4, 6-4.
Williams, runner-up last year, had no problems in a 6-2, 6-4 win over Russian Elena Vesnina.
Next up for Wozniacki is Czech fourth seed Barbora Zahlavova Strycova, who beat American Coco Vandeweghe 6-4, 7-5.
Vandeweghe, the seventh seed, served for the second set at 5-3, but she lost the final four games to be beaten.
Williams, the tournament’s third seed, was dominant on the hard courts. Next up: compatriot Lauren Davis, who overcame Poland’s Urszula Radwanska 2-6, 6-2, 6-1.
