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The 17-year-old qualifier, ranked 296th, won 5-7, 6-4, 6-4, leaping into the air in celebration after converting her fourth match point.
Duval was playing in just her second Grand Slam match. She also faced a former US Open champion, Kim Clijsters, in the first round at Flushing Meadows last year.
She was facing a top-20 opponent for the first time on Tuesday.
The 11th-seeded Stosur had reached at least the quarter-finals in her last three trips to the US Open. She had 56 unforced errors.
Duval was born in Miami but lived in Haiti until she moved back to the United States at age 8.
US Open results on Tuesday at Flushing Meadows (x denotes seeded player):
Men
1st rd
Novak Djokovic (SRB x1) bt Ricardas Berankis (LTU) 6-1, 6-2, 6-2
Benjamin Becker (GER) bt Lukas Rosol (CZE) 6-3, 3-6, 6-3, 6-4
Jarkko Nieminen (FIN) bt Lukasz Kubot (POL) 7-5, 7-5, 6-2
Joao Sousa (POR) bt Grigor Dimitrov (BUL x25) 3-6, 6-3, 6-4, 5-7, 6-2
Tommy Haas (GER x12) bt Paul-Henri Mathieu (FRA) 6-4, 6-4, 6-1
Lu Yen-Hsun (TPE) bt Daniel Gimeno (ESP) 6-4, 7-6 (7/5), 6-3
Donald Young (USA) bt Martin Klizan (SVK) 6-1, 6-0, 6-1
Florian Mayer (GER) bt Juan Monaco (ARG x28) 6-4, 6-2, 3-0, retired
Tobias Kamke (GER) bt Steve Johnson (USA) 6-7 (4/7), 6-4, 7-6 (9/7), 6-2
Denis Istomin (UZB) bt Nicolas Almagro (ESP x15) 6-3, 6-1, 4-6, 6-3
Julien Benneteau (FRA x31) bt Michal Przysiezny (POL) 6-4, 5-7, 6-4, 6-4
Jeremy Chardy (FRA) bt Sergiy Stakhovsky (UKR) 6-4, 4-6, 6-2, 4-6, 6-4
Denis Kudla (USA) bt Jiri Vesely (CZE) 6-2, 6-2, 6-7 (6/8), 7-5
Tomas Berdych (CZE x5) bt Paolo Lorenzi (ITA) 6-1, 6-4, 6-1
Pablo Andujar (ESP) bt Thiemo de Bakker (NED) 6-4, 6-4, 6-4
Milos Raonic (CAN x10) bt Thomas Fabbiano (ITA) 6-3, 7-6 (8/6), 6-3
Maximo Gonzalez (ARG) bt Jerzy Janowicz (POL x14) 6-4, 6-4, 6-2
Jack Sock (USA) bt Philipp Petzschner (GER) 7-6 (7/2), 3-6, 5-2, retired
Roger Federer (SUI x7) bt Grega Zemlja (SLO) 6-3, 6-2, 7-5
Carlos Berlocq (ARG) bt Santiago Giraldo (COL) 6-3, 3-6, 6-7 (6/8), 6-4, 6-2
Adrian Mannarino (FRA) bt Horacio Zeballos (ARG) 4-6, 6-4, 6-2, 6-1
Sam Querrey (USA x26) bt Guido Pella (ARG) 7-6 (7/3), 4-6, 6-1, 6-2
John Isner (USA x13) bt Filippo Volandri (ITA) 6-0, 6-2, 6-3
Gael Monfils (FRA) bt Adrian Ungur (ROM) 6-1, 6-2, 6-0
Edouard Roger-Vasselin (FRA) bt Albert Montanes (ESP) 6-3, 6-2, 6-4
Philipp Kohlschreiber (GER x22) bt Collin Altamirano (USA) 6-1, 6-3, 6-1
Rogerio Dutra Silva (BRA) bt Vasek Pospisil (CAN) 4-6, 3-6, 7-6 (11/9), 6-2, 7-6 (12/10)
Women
1st rd
Caroline Wozniacki (DEN x6) bt Duan Ying-Ying (CHN) 6-2, 7-5
Chanelle Scheepers (RSA) bt Chanel Simmonds (RSA) 2-6, 6-2, 6-1
Camila Giorgi (ITA) bt Jana Cepelova (SVK) 6-2, 6-2
Hsieh Su-Wei (TPE) bt Klara Zakopalova (CZE x31) 6-3, 6-3
Elena Vesnina (RUS x22) bt Annika Beck (GER) 6-1, 6-1
Karin Knapp (ITA) bt Grace Min (USA) 6-3, 6-1
Lucie Safarova (CZE) bt Lesya Tsurenko (UKR) 6-3, 2-6, 6-4
Roberta Vinci (ITA x10) bt Timea Babos (HUN) 6-4, 6-2
Maria Kirilenko (RUS x14) bt Yanina Wickmayer (BEL) 6-1, 6-1
Michelle Larcher de Brito (POR) bt Eleni Daniilidou (GRE) 6-4, 6-3
Donna Vekic (CRO) bt Mariana Duque (COL) 7-6 (7/5), 4-6, 6-2
Simona Halep (ROM x21) bt Heather Watson (GBR) 4-6, 6-4, 6-2
Svetlana Kuznetsova (RUS x27) bt Mallory Burdette (USA) 6-3, 7-5
Peng Shuai (CHN) bt Yvonne Meusburger (AUT) 6-3, 6-4
Flavia Pennetta (ITA) bt Nicole Gibbs (USA) 6-0, 6-2
Sara Errani (ITA x4) bt Olivia Rogowska (AUS) 6-0, 6-0
Petra Kvitova (CZE x7) bt Misaki Doi (JPN) 6-2, 3-6, 6-1
Bojana Jovanovski (SRB) bt Andrea Petkovic (GER) 6-2, 6-4
Alison Riske (USA) bt Tsvetana Pironkova (BUL) 6-3, 6-3
Mona Barthel (GER x28) bt Johanna Larsson (SWE) 6-1, 6-4
Julia Glushko (ISR) bt Nadia Petrova (RUS x20) 6-3, 6-4
Sachia Vickery (USA) bt Mirjana Lucic (CRO) 6-4, 6-4
Daniela Hantuchova (SVK) bt Maria Sanchez (USA) 7-5, 6-2
Victoria Duval (USA) bt Samantha Stosur (AUS x11) 5-7, 6-4, 6-4
Ana Ivanovic (SRB x13) bt Anna Tatishvili (GEO) 6-2, 6-0
Alexandra Dulgheru (ROM) bt Varvara Lepchenko (USA) 6-7 (5/7), 6-2, 7-6 (7/5)
Christina McHale (USA) bt Julia Gorges (GER) 6-4, 6-3
Elina Svitolina (UKR) bt Dominika Cibulkova (SVK x17) 6-4, 6-3
Alize Cornet (FRA x26) bt Maria Joao Koehler (POR) 6-3, 6-2
Ajla Tomljanovic (CRO) bt Casey Dellacqua (AUS) 3-6, 6-1, 6-4
Aleksandra Wozniak (CAN) bt Vesna Manasieva (SRB) 7-5, 7-6 (7/5)
Victoria Azarenka (BLR x2) bt Dinah Pfizenmaier (GER) 6-0, 6-0
