Third-seeded Stosur, who won this tournament in 2009, could only convert seven of her 15 break-point opportunities but eventually won in two hours and 13 minutes at Utsubo Tennis Center.
Bouchard started the match well, jumping out to a 6-3, 4-3 lead. On two occasions she was six points away from capturing her first-ever WTA title.
Stosur, the U.S. Open champion in 2011, broke Bouchard's serve at 5-5 in the second set and never looked back en route to collecting her fifth career title and second this season.
It was the 17th tour final for the 29-year-old Stosur but the first of Bouchard's career.
Bouchard is the first Canadian to reach a WTA singles final since Vancouver's Rebecca Marino at Memphis in 2011. The 19-year-old was trying to become the first Canadian title winner on Tour since Aleksandra Wozniak at Stanford in 2008.
Stosur lost her only previous match with the 19-year-old Bouchard last April in Charleston when she retired due to injury while trailing 6-1 2-0.