Two-time US Open champion Venus Williams beat Kirsten Flipkens 6-1, 6-2 on the opening day in Flushing Meadows, New York.
The 11th seed Kei Nishikori was the casualty on the opening day in New York, losing to the Brit Daniel Evans 6-4, 6-4, 6-2.
Agnieszka Radwanska had no trouble beating Spain's Silvia Soler-Espinosa. The Pole won 6-1, 6-2.
Chinese ace Li Na made little work of Olga Govortsova in a 6-2, 6-2 straight-set win.
Defending champion Serena Williams dropped just one game in her 6-0, 6-1 demolition job against Francesca Schiavone.
World No. 2 Rafael Nadal proved too hot to handle for American Ryan Harrison who was beaten 6-4, 6-2, 6-2.
David Ferrer overcame opening-set jitters to beat Nick Kyrgios of Australia 7-5, 6-3, 6-2.
American hope Sloane Stephens continued to impress as she came from behind to beat Mandy Minella 4-6, 6-3, 7-6.