Schnyder, seeded fifth, took the first set 6-4 then held on to win the second 7-6 (7-2) on the hard courts at Connecticut Tennis Center in New Haven.
Meanwhile, in an upset, Dane Caroline Wozniacki notched a win when eighth-seeded Slovakian Dominika Cibulkova retired due to a heat-related illness after losing the first set 7-6 (9-7).
In other first-round action, Sara Errani defeated American qualifier Mallory Cecil 6-2, 4-6, 7-6 (7-1), Romanian Sorana Cirstea rallied against Russian Alla Kudryavtseva 4-6, 6-3, 7-5 and Slovenian Katarina Srebotnik downed Spain's Maria Jose Martinez Sanchez 6-7 (4-7), 6-3, 6-2.
Last year's winner, Russian Svetlana Kuznetsova is not defending her title this week where the top seed is Russian Anna Chakvetadze.
The $600,000 event is a final U.S. Open tune-up.