Serena Williams needed only 60 minutes to dispatch Francesca Schiavone 6-0, 6-1, capitalizing on eight double-faults by her Italian opponent.
Venus Williams, who won the U.S. Open in 2000 and 2001, now goes on to meet China's Zheng Jie.
Also Monday, Poland's Agnieszka Radwanska, last year's runner-up at Wimbledon, cruised past Spaniard Silvia Soler-Espinosa 6-1, 6-2 at Arthur Ashe Stadium. Her Round 2 opponent will be Spaniard Maria-Teresa Torro-Flor.
In other Day 1 action, fifth-seeded Li Na of China moved on with a 6-2, 6-2 rout of Belarusian Olga Govortsova; No. 8 Angelique Kerber of Germany breezed by Czech Lucie Hradecka 6-1, 6-1; and No. 9 Jelena Jankovic of Serbia eased past American Madison Keys 6-3, 6-4.
Among the other seeded winners were No. 15 American Sloane Stephens, No. 16 Sabine Lisicki of Germany, No. 18 Spaniard Carla Suarez Navarro, No. 19 Romanian Sorana Cirstea and No. 23 American Jamie Hampton, who claimed her first-ever U.S. Open win with 6-4, 6-2 decision over Spaniard Lara Arruabarrena.
No. 25 Estonian Kaia Kanepi, No. 30 Briton Laura Robson and No. 32 Russian Anastasia Pavlyuchenkova also advanced with Monday triumphs, as did Austrian Patricia Mayr-Achleitner and American Coco Vandeweghe.
2014: The Year in Music [PHOTOS]