The Kazakh cruised past a potentially dangerous first round opponent in Kostyuk as she only dropped three games on her way to the second round.
Rybakina hasn’t traditionally done well in New York but will be looking to change that this year and next up for the fourth seed is Panna Udvardy or Ajla Tomljanovic.
In the big first round clash, former US Open champion Sloane Stephens crashed out to 19th seed Beatriz Haddad Maia. After easily losing the first set 6-2, Stephens battled back as she edged to the second set 7-5 as she looked to use her home crowd to her advantage.
However it was too little too late as Haddad Maia won the deciding set 6-4 and claimed a place in the second round.
Another tough match awaits the Brazilian in the second round when she takes on Taylor Townsend, who defeated Varvara Gracheva.
There was also an early exit for Veronika Kudermetova who went out in straight sets to Bernarda Pera.
