Nineteen-year-old Canadian Bouchard, competing in her first WTA Tour final, looked to be on course for her first crown when she breezed through the first set.
But the 29-year-old Australian got back on level terms after securing the crucial break of serve in game 11 of the second set, and then stormed through the third to claim a 3-6 7-5 6-2 victory.
"Eugenie was playing really well today," said Stosur, who reeled off four straight games - after Bouchard had held her opening service game in the decider - en route to her second Osaka title.
The 2011 US Open champion continued on www.wtatennis.com: "I just had to stick it out in the second set, and I'm pretty happy with how things went in the third.
"I love playing here. I love the site and the fans are great - I always feel like I have lots and lots of support when I come to Osaka."