The Australian, who beat Serena Williams last year for her first Grand Slam, powered back to 5-5 in the third-set decider, just two points from the semi-finals, before the next two points gave world number one Victoria Azarenka a 6-1 4-6 7-6 victory.
"That proves to me that I am capable of doing it," Stosur said after her rousing comeback produced high drama and cheers for her on Arthur Ashe Stadium court. "To have another showing here at the Open like this, it for sure gives me confidence to think that maybe one day I can do it again."
Stosur entered the match having lost all six previous matches against the deep-hitting baseliner in straight sets, but with her back to the wall on Tuesday, the 28-year-old Australian began finding the corners with her big groundstrokes.
"I guess going into a match like that where you've never beaten a player before, you've got to just play well and really get everything out of yourself that you can," said Stosur.
"That's what I did today and just came up short. It's disappointing, but at least I know that I came within a whisker of getting there today."
After clawing back to level the tension-packed match at 5-5 in the third-set tiebreaker, seventh-seeded Stosur hit a net cord ball that sat up for Azarenka, who sliced a drop shot winner over the net to reach match point.
Azarenka then ripped a deep groundstroke that brushed the line and drew a wide backhand from Stosur that ended the thriller after two hours 23 minutes.
"There's always going to be disappointment when you lose in the quarters of the US Open, but I have to say I'm really pleased with the way I played," said Stosur. "I thought it was a really, really good match ... I gave it everything I had."