Samantha Stosur, the 2011 US Open winner, eased past Timea Babos 6-3 6-4.
Stosur advanced with ease and will now face Russian Evgeniya Rodina, as the Australian ended a run of poor form over her past few tournaments.
Two-time US Open finalist Victoria Azarenka made a winning start to her 2015 campaign after she swatted aside Lucie Hradecka 6-1 6-2 in the first round.
Former world number one Azarenka - seeded 20th at Flushing Meadows - only lost three games and broke serve four times throughout Tuesday's contest as she earned a showdown with Yanina Wickmayer, who downed Francesca Schiavone 6-3 6-1.
Azarenka's routine win was not without drama, however, after the Belarusian reacted angrily to a bad line call, calling out to the umpire: "You're kidding me? Have you ever played tennis? You did? You probably weren't very good."
Azarenka is joined in the second round by second seed Simona Halep, who was leading 6-2 3-0 when Marina Erakovic retired.
Last year's finalist and fourth seed Caroline Wozniacki encountered no problems against American wildcard Jamie Loeb, the Dane winning 6-2 6-0.
Wozniacki – who like Azarenka is a two-time finalist at Flushing Meadows – was rarely troubled by her 20-year-old opponent and raced through the encounter in 66 minutes with a stunning show of power.
Czech fifth seed Petra Kvitova was efficient in a 6-1 6-1 win over Laura Siegemund.
Andrea Petkovic was given a real scare by Caroline Garcia as the German lost the opening set, but the 18th seed dug deep and came firing back to win 3-6 6-4 7-5.
Fellow seeds Angelique Kerber (11th) and Garbine Muguruza (ninth) both cruised to straight-sets victories.
Kerber accounted for Alexandra Dulgheru 6-3 6-1, while Muguruza claimed her first win since Wimbledon after downing Carina Witthoeft 6-2 6-4.
Sabine Lisicki ousted Aliaksandra Sasnovich 6-1 6-4.
Sixth seed Lucie Safarova and 14th seed Timea Bacsinszky stuttered in their opening matches and became the latest seeds to be dumped out, following a handful on Monday.
Safarova went down 6-4 6-1 to Lucie Tsurenko and Barbora Strycova upstaged Bacsinszky 7-5 6-0.
Irina-Camelia Begu also crashed out following a 6-1 0-6 7-6 (7-3) loss to Olga Govortsova, while Alize Cornet fell to Kurumi Nara 2-6 6-4 6-4.
Meanwhile, there were straight-set victories for Sara Errani (6-0 6-1 against Mayo Hibi), Flavia Pennetta (6-1 3-6 6-1 over Jarmila Gajdosova), Johanna Konta (6-3 6-0 against Louisa Chirico), Wang Qiang (7-5 6-2 over Maria Sakkari), Varvara Lepchenko (6-1 6-1 against Kirsten Flipkens), Camila Giorgi (6-3 6-3 over Johanna Larsson), Kateryna Bondarenko (6-0 6-3 against Yulia Putintseva), and Anna-Karolina Schmiedlova (6-3 6-4 over Julia Goerges).
Karin Knapp rallied to beat Ajla Tomljanovic 6-7 (1-7) 6-2 6-4, while Elena Vesnina, Jelena Ostapenko, Petra Cetkovska, Danka Kovinic and Mona Barthel also needed three sets.
British hope Laura Robson fell to Vesnina 3-6 6-3 7-5, Ostapenko outlasted Annika Beck 6-4 1-6 6-4, Cetkovska eliminated Christina McHale 4-6 6-4 6-3, Kovinic recovered to defeat Aleksandra Krunic 4-6 7-5 6-1 and Barthel saw off Tsvetana Pironkova 5-7 7-6 (7-4) 6-1.
Evgeniya Rodina made light work of Tereza Mrdeza 6-2 6-2, Nicole Gibbs was too good for Lourdes Dominguez Lino 6-3 3-6 6-4, Shelby Rogers beat Sachia Vickery 6-2 6-2 and Monica Niculescu prevailed 7-6 (7-3) 5-7 6-3 against Alexandra Panova 7-6 (7-3) 5-7 6-3.