Spanish 25th seed Garbine Muguruza was the only top player to suffer defeat on the opening day at Flushing Meadows, with Halep and Wozniacki progressing despite dropping sets.
Muguruza fell 6-3 7-6 (7-4) to Croatian qualifier Mirjana Lucic-Baroni.
Romanian second seed Halep overcame a spirited challenge from American wildcard Danielle Rose Collins 6-7 (2-7) 6-1 6-2, while Denmark's 10th seed Wozniacki advanced when opponent Magdalena Rybarikova retired injured with the former world number one leading 6-1 3-6 2-0.
Russian fifth seed Maria Sharapova came from 4-2 down in the first set to canter to a 6-4 6-0 victory over compatriot Maria Kirilenko in the night session.
Earlier, Polish fourth seed Agnieszka Radwanska reeled off 12 straight games in a 6-1 6-0 thrashing of Canada's Sharon Fichman.
Fichman won just three points in the second set, as Radwanska stormed into the second round.
American 19th seed Venus Williams won the battle of the veterans, downing Japan's Kimiko Date-Krumm 2-6 6-3 6-3.
Between Williams and Date-Krumm, there was 77 years of life experience on Arthur Ashe Stadium, and the two-time champion eventually won through despite a valiant challenge from Date-Krumm, 43.
Williams' compatriot and 21st seed Sloane Stephens put in a commanding performance to beat Germany's Annika Beck 6-0 6-3.
German sixth seed Angelique Kerber was pushed all the way by Russia's Ksenia Pervak, before prevailing 6-2 3-6 7-5.
Jelena Jankovic hit 21 winners on her way past fellow Serbian Bojana Jovanovski, the ninth seed winning 6-2 6-3.
Andrea Petkovic, the 18th seed of Germany, fended off Tunisian qualifier Ons Jabeur 7-6 (9-7) 1-6 6-3.
French 22nd seed Alize Cornet beat countrywoman and wildcard Amandine Hesse 6-1 6-2, while Japan's Kurumi Nara - the 31st seed - thrashed Canadian Aleksandra Wozniak 6-2 6-1.
Sara Errani, the 13th seed of Italy, eased past in-form Belgian Kirsten Flipkens 6-1 7-5, and Germany's 26th seed Sabine Lisicki defeated Francoise Abanda 6-3 7-5.
Roberta Vinci joined countrywoman Errani in the second round, the 28th seed dismissing Argentina Paula Ormaechea 6-3 6-3.
Wimbledon semi-finalist Lucie Safarova had the better of Hungary's Timea Babos, the Czech 14th seed progressing 6-4 7-5.
In unseeded match-ups, there were mixed results for the Israeli contingent as Shahar Peer beat Great Britain's Johanna Konta 6-2 6-3 but qualifier Julia Glushko was humbled by American wildcard Madison Brengle 6-3 6-2.
China's Peng Shuai defeated compatriot Zheng Jie 6-3 6-3, while Slovakian veteran Daniela Hantuchova posted a come-from-behind win over Swiss Romina Oprandi 4-6 6-2 6-3.
Australian qualifier Anastasia Rodionova upended Italy's Camila Giorgi 1-6 7-5 6-3, and Chinese qualifier Zheng Saisai similarly overcame a slow start to down Swiss Stefanie Voegele 1-6 6-2 6-2.
Romania's Irina-Camelia Begu got past Spain's Silvia Soler-Espinosa 7-6 (7-4) 6-3, Russia's Alla Kudryavtseva battled through against China's Duan Ying-Ying 2-6 6-2 6-4 and Swiss Timea Bacsinszky was fortunate to progress when opponent Kiki Bertens retired with the score 7-6 (9-7) 3-4 in the Dutchwoman's favour.
Joining Bacsinszky in the second round was compatriot Belinda Bencic, the 17-year-old downing Belgium's Yanina Wickmayer 6-3 6-2.
Puerto Rico's Monica Puig was too good for Czech Tereza Smitkova 3-6 6-3 6-3, while Belarusian qualifier Aliaksandra Sasnovich was a 6-4 6-3 victor over Slovakia's Anna Schmiedlova.
Alexandra Dulgheru, of Romania, downed Czech Kristyna Pliskova 6-3 6-4, Bulgaria's Tsvetana Pironkova beat Italian Karin Knapp 6-4 6-3 and Slovakian Jana Cepelova eventually got over the line against Spain's Maria-Teresa Torro-Flor 2-6 7-5 6-1.
Swede Johanna Larsson dealt France's Virginie Razzano an embarrassing 6-0 6-0 result.