Bidding to make the main draw for the first time at an overseas grand slam, Jones upset American 10th seed Bernarda Pera 6-1 4-6 6-2 to notch her maiden win at Flushing Meadows.
After reaching the final round of qualifying at Wimbledon, the former world No.1 junior next faces lower-ranked Brazilian Laura Pigossi bidding to emulate that feat.
Astra Sharma and Maddison Inglis also progressed to round two of women's qualifying.
Sharma beat Serbian Lola Radivojevic 7-5 6-4, while Inglis defeated Storm Hunter 6-3 6-4 in an all-Aussie affair.
But Arina Rodionova lost 6-1 7-5 to Croatian Tara Wuerth.
James Duckworth and James McCabe advanced in men's qualifying.
Fifth-seeded Duckworth downed Argentine Facundo Bagnis 6-4 6-2, while McCabe rallied for a 6-3 6-7 (2-7) 6-4 win over Italian Francesco Maestrelli.
But Omar Jasika bowed out 6-7 (3-7) 6-3 6-3 to Frenchman Hugo Grenier.
Eight more Australians, including Bernard Tomic and Daria Saville, will open their qualifying campaigns on Wednesday (AEST).
Back up to No.169 in the world after almost spiralling outside the top 1000, 32-year-old Tomic plays American Patrick Kypson in his quest to reach a grand slam main draw for the first time since successfully qualifying for the 2021 Australian Open.
The 2009 US Open junior champion hasn't featured in the Flushing Meadows main draw in nine years.
But he has arrived in New York in strong form, fresh off winning a Challenger event in Colombia.
The qualifiers are hoping to join a dozen Australian direct entrants, led by men's world No.8 Alex de Minaur, and wildcards Tristan Skoolkate and Tahlia Gibson.
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