Coco Gauff, the 2023 US Open champion, fought through a tough three-set match to beat Australia’s Ajla Tomljanovic.
The win came despite Gauff’s ongoing struggles with her serve, which she recently tried to fix by hiring a new biomechanics expert.
World number two Iga Swiatek had a much easier time, cruising to a comfortable victory over Emiliana Arango.
In other results, Amanda Anisimova and two-time champion Naomi Osaka both won, while Danielle Collins was eliminated.