Stosur kept her composure as Williams erupted in anger at the chair umpire in the second set yesterday, dominating the 13-time Grand Slam champion who had reached the final without dropping a set.
She became the first Australian woman to take the title in New York since Margaret Court in 1973, and the first to win a Grand Slam since Evonne Goolagong won Wimbledon in 1980.
"I had one of my best days and I'm very fortunate that I had it on this stage in New York," Stosur said. "Ever since I started playing it was a dream of mine to be here one day."
Williams arrived in the final after dismantling world number one Caroline Wozniacki in the semi-finals on Saturday night in a match that dragged toward midnight.
"I was more tired than I expected," Williams said. "But I want to give all credit to Sam today ... She played really, really well. That's what you have to do when you play a Grand Slam final."
Stosur, playing her second career Grand Slam final after a runner-up finish in the French Open last year, quickly claimed the opening set, breaking Williams to lead 2-1 and winning the last 12 points of the set as Williams' frustration grew.
Williams, whose powerful serve is a cornerstone of her game, struggled to get her first serves in and Stosur repeatedly made her pay.