Meanwhile, defending champion Naomi Osaka beat Anna Blinkova in three sets and 15-year-old Cori Gauff also progressed but former champion Sloane Stephens was knocked out.
Here, PA looks back at day two and forward to day three of the tournament.
Shot of the day
Jo-Wilfried Tsonga showed he has still got it at the net, even if he blew a two-set lead against Tennys Sandgren.
Stat of the day
Wimbledon champion Simona Halep won her first match at Flushing Meadows since 2016.
Quote of the day
Shock of the day
Fourth seed Dominic Thiem has been struggling with a virus but the Austrian will still be disappointed at tumbling out in the first round to unseeded Italian Thomas Fabbiano.
British number one Kyle Edmund was unable to join Johanna Konta and Dan Evans in round two after crashing out in five sets to Pablo Andujar of Spain.
Konta and Evans are back in action on Wednesday.
Men: Dominic Thiem (4), Stefanos Tsitsipas (8), Karen Khachanov (9), Roberto Bautista Agut (10), Felix Auger Aliassime (18), Kyle Edmund (30)
Women: Sloane Stephens (11), Garbine Muguruza (24), Carla Suarez Navarro (28), Barbora Strycova (31)
Wednesday's order of play
Arthur Ashe Stadium:
Marium Bolvadze v Karolina Pliskova
Roger Federer v Damir Dzumhur
Novak Djokovic v Juan Ignacio Londero
Serena Williams v Catherine McNally
Louis Armstrong Stadium:
Bradley Klahn v Kei Nishikori
Elina Svitolina v Venus Williams
Lin Zhu v Madison Keys
Lauren Davis v Ashleigh Barty
Borna Coric v Grigor Dimitrov
Johanna Konta v Margarita Gasparyan
Dan Evans v Lucas Pouille