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 with a forehand winner.
Duval was playing in just her second Grand Slam match. She also faced a former U.S. Open champ, Kim Clijsters, in the first round at Flushing Meadows last year.
She was facing a top-20 opponent for the first time Tuesday.
"I know she didn't play her best today, and this is the best I've played in my career, so I'm really excited," Duval told the Louis Armstrong Stadium crowd. "I just tried to stay in the moment."
The 11th-seeded Stosur had reached at least the quarterfinals in her last three trips to the U.S. 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. She trains in Bradenton, Fla.
For all of one game, and only one game, Victoria Azarenka faced a bit of a test in the first round. After needing 10 minutes to break serve at the outset, the second-seeded Azarenka breezed the rest of the way, putting together a 6-0, 6-0 victory over 99th-ranked Dinah Pfizenmaier of Germany.
The match was played in Arthur Ashe Stadium, where Azarenka lost in three sets to Serena Williams in last year's final at Flushing Meadows.
This one was far, far less competitive or gripping, except perhaps for the opening game, which lasted 18 points spread over 10 minutes, until two-time Australian Open champion Azarenka converted her sixth break point. The rest of the match took a total of 55 minutes.
"There are things, you know, I feel like should be better," Azarenka said. "But overall, it's a good start."
Kvitova won 6-2, 3-6, 6-1 on a windy day at Arthur Ashe Stadium.
"I like big matches on the big stadium, but the people -- it's too much crowds for myself, I think," she said.
Kvitova has reached at least the semifinals at the other three major events; she has never made it past the fourth round at Flushing Meadows.
She's also struggled in the North American swing leading up to the U.S. Open, but she made a breakthrough last year. Kvitova won two of those tournaments and reached the semifinals at another in 2012, then matched her longest run at the year's last Grand Slam tournament.
"So I have good motivation to improve my results here," she said.
The final set Tuesday was closer than the score in this rare matchup of two lefties. After Kvitova went up a break at 2-0, Doi had a chance to break right back but couldn't convert.
Two years ago, Kvitova became the first reigning Wimbledon women's champion to lose her first U.S. Open match in the same season. She was in danger of another early exit Tuesday when she made 15 unforced errors in the second set.
But she's hardly fazed by three-set matches. Kvitova recently played six straight across three tournaments, winning four of them.
Doi, from Japan, fell to 0-4 against top 10 opponents.
Also Tuesday, sixth-seeded Caroline Wozniacki held off qualifier Duan Ying-Ying to win her first-round match.
With boyfriend Rory McIlroy in the stands, Wozniacki fought off a set point in the second to win 6-2, 7-5 on Tuesday.
The 133rd-ranked Duan had a chance to serve out the set at 5-3 in her Grand Slam debut. But the 2009 U.S. Open finalist broke back. Then Duan had a set point on Wozniacki's serve that she couldn't convert.
Wozniacki broke serve in the next game, then staved off three break points to clinch the win.
Errani, the 2012 French Open runner-up and a semifinalist at Flushing Meadows last year, needed 51 minutes in Armstrong Stadium to dispatch her 151st-ranked opponent, who lost in qualifying but made it into the main draw when Ayumi Morita withdrew with an injury.
Errani won 54 points to 23 for Rogowska.
No. 10-seeded Roberta Vinci overcame some shaky serving to win her first-round match in straight sets. The Italian, a quarterfinalist at Flushing Meadows last year, beat Timea Babos 6-4, 6-2. Babos converted all three of her break points, but Vinci broke the Hungarian's serve six times.
Vinci reached a career-high ranking this summer at age 30. She made the round of 16 at the French Open and Wimbledon this year.
No. 13-seeded Ana Ivanovic and 14th-seeded Maria Kirilenko got off to quick starts, each winning in under an hour. Ivanovic, the 2008 French Open champ, beat Anna Tatishvili 6-2, 6-0. Kirilenko won 6-1, 6-1 against Yanina Wickmayer, a semifinalist at Flushing Meadows four years ago whose ranking has fallen to 57th.
Information from The Associated Press was used in this report.