Ukrainian fourth seed Elina Svitolina beat Russia's Evgeniya Rodina to safely progress to the US Open third round.
Svitolina won 6-4 6-4 in one hour and 22 minutes on Arthur Ashe Stadium.
Latvia's French Open champion, 12th seed Jelena Ostapenko, also reached round three with a 6-4 6-4 win over Romanian Sorana Cirstea.
American world number 91 Jennifer Brady thrashed Czech Republic's 23rd seed Barbora Strycova 6-1 6-1 in just 56 minutes in New York.