It was quick and easy for top seed Lucie Safarova as she opened her Coupe Banque Nationale campaign, while Tatjana Maria also advanced to the second round.
After reaching the last 16 at the US Open, Safarova crushed Anna Tatishvili 6-0 6-1 in Quebec City on Tuesday.
Safarova broke six times and lost just four points on serve against the American at the WTA International tournament.
Maria - the fourth seed - rallied from a break down in the second set to beat Fanny Stollar 6-2 7-6 (7-4).
Belgian seventh seed Alison Van Uytvanck came from a set behind to prevail 4-6 6-2 7-6 (7-1) against Canada's Carol Zhao.
Jennifer Brady was not so fortunate, the sixth seed beaten 6-3 6-2 by Bianca Andreescu.
Lucie Hradecka, Sachia Vickery, teenager Sofia Kenin - who faced returning former world number one Maria Sharapova at Flushing Meadows - Viktorija Golubic and Francoise Abanda won through to the next round.