"There's a lot to be thankful for. I don't take anything for granted. ... My Dad is really fortunate to be here," she told the Louis Armstrong Stadium crowd during an on-court interview.
Duval, who needed to go through qualifying to get into the U.S. Open because her ranking is so low, joined eight other American women in the second round of the main draw. Tuesday also was a good day for American men, who went 5-2, led by No. 13 John Isner and No. 26 Sam Querrey.
"We're obviously trying to make American tennis become what it used to be," Duval said. "We're all working toward the same goal. We're all a tight-knit group. Helping each other is important. I think we're on an amazing path."
A group of Americans is slated to play Wednesday, when there will be a mix of first- and second-round matches, including past champions Serena and Venus Williams, 15th-seeded Sloane Stephens, 23rd-seeded Jamie Hampton, and 33-year-old James Blake, who announced the U.S. Open will be the last tournament of his career. Also on the schedule: Andy Murray, the defending men's champion who added a Wimbledon championship last month.
Until Tuesday, Duval did not own a victory over anyone ranked higher than 69th. She had not faced a woman in the top 20. She only had played one match at a major tournament, a first-round loss to Kim Clijsters at last year's U.S. Open (which turned out to be the final singles victory of the Belgian's career).
Stosur was unhappy with the way she played Tuesday, including 10 double-faults and a total of 56 unforced errors, 21 more than Duval.
"I'm not going to be a sore loser and say she didn't do anything," said Stosur, an Australian. "But, you know, I think I certainly helped her out there today, that's for sure."