Stosur lost her serve six times, including three times in dropping the first set. But she overcame two second-set breaks with three of her own, including in the 12th game that left the match even.
Stosur had two more breaks in a four-game winning streak that put her up 4-1 in the third set and soon finished off her sixth WTA title.
Stosur is 5-12 in WTA finals, adding the Osaka title to a win in August at Carlsbad, Calif.
Bouchard, at No. 35 the highest ranked teenager in the WTA, was marking her first WTA finals appearance.
The championship came with a $40,000 check for Stosur, who has won nearly $12.7 million in her career. Bouchard, after collecting $20,000 Sunday, passed the $500,000 in career winnings.