Wimbledon champion Serena Williams, a three-time U.S. Open champion and No. 4 seed this year, knocked off fellow American Coco Vandeweghe 6-1, 6-1.
Williams notched nine winners and converted all three of her break-point chances.
Unseeded Venus Williams ousted another American, Bethanie Mattek-Sands, 6-3, 6-1.
Second-seeded Agnieszka Radwanska of Poland advanced earlier in the day with a 6-1, 6-1 win over Russia's Nina Bratchikova in a match that whizzed by in 54 minutes.
The big upset of the day was Romanian Irina-Camelia Begu's 6-2, 6-2 win over eight-seeded Caroline Wozniacki of Denmark.
Sixth-seeded Angelique Kerber of Germany was a 6-2, 6-0 winner over Britain's Anne Keothavong. Kerber and Venus Williams square off Thursday.
Among the other seeded players advancing to the second round were No. 12 Ana Ivanovic of Serbia, who logged a 6-3, 6-2 win over Ukrainian Elina Svitolina, and No. 20 Roberta Vinci of Italy, who sped past Urszula Radwanska 6-1, 6-1.
Celebrity Families of 2014 [PHOTOS]