The 29-year-old Romanian 12th seed defeated Italy's Camila Giorgi 6-4, 7-6 (7/3) to book a second-round match against Slovakian lucky loser Kristina Kucova, who ousted American Ann Li 7-5, 6-1.
Halep, the 2018 French Open and 2019 Wimbledon champion, tore a left calf muscle at the Italian Open, missed the French Open and Wimbledon, then suffered a right thigh injury at Cincinnati, but made a solid New York start.
Halep fired six aces and won 83% of her first serve points, hitting 14 winners against 16 unforced errors while taking advantage of 31 unforced errors by Giorgi.
Defending champion Naomi Osaka, seeking her third US Open crown in four years, was set for the feature night match at Arthur Ashe Stadium against 87th-ranked Czech Marie Bouzkova.
Osaka won their only prior meeting in the first round of this year's Australian Open on the way to her fourth Grand Slam title.
The 23-year-old Japanese star could become the first back-to-back US Open women's champion since Serena Williams won her third in a row in 2014.
Osaka enters on a 15-match Grand Slam win streak, having skipped the French Open last year and Wimbledon this year and withdrawn after a first-round win at this year's French Open over mental health issues.
Also on the night schedule is second seed Aryna Sabalenka of Belarus against Serbia's Nina Stojanovic.
Americans Sloane Stephens and Madison Keys meet in a first-round rematch of the 2017 US Open final won by Stephens.
On the men's side, while top-ranked Novak Djokovic waits until Tuesday to begin his quest for a US Open crown to complete a calendar-year Grand Slam, his top-seeded rivals take the court.
Greek third seed Stefanos Tsitsipas will face three-time Grand Slam winner Andy Murray of Britain at Arthur Ashe Stadium.
Murray, ranked 112th, won the 2012 US Open and 2013 and 2016 Wimbledon crowns. He would be the lowest-ranked player to ever beat a top-three foe at the US Open since the rankings began in 1973.
Two-time Olympic champion Murray is 14-0 in prior US Open first-round matches and the 34-year-old Scotsman seeks his biggest win since downing then-world number two Novak Djokovic in the 2016 ATP Finals.
Tsitsipas, the French Open runner-up, is Murray's highest-ranked foe since he lost to third-ranked Stan Wawrinka in a 2017 French Open semi-final
Russian second seed Daniil Medvedev opens in the Ashe night finale against Frenchman Richard Gasquet.
Medvedev, the 2019 US Open and 2021 Australian Open runner-up, seeks his 200th career match win and his 160th on hardcourts.
Gasquet is 1-35 against top-two rivals, having dropped 35 in a row since beating then-number one Federer in 2005 at Monte Carlo.
Croatia's 221st-ranked Ivo Karlovic, at 42 the oldest US Open qualifier in the Open Era (since 1968), would become the oldest player to defeat a top-10 foe if he can upset Russian fifth seed Andrey Rublev.