American 20-year-old Kenin produced a pivotal break at 4-4 in the second set, which came as she reeled off seven games in succession to turn the match on its head.
The No.3 seed went a break up in the opener but surrendered her advantage and lost out in the tie-break when she sent a forehand from the baseline long.
Stosur, who was looking for her first WTA Tour singles title in more than two years, dropped her serve at the start of the second but gave up just one point across three games to edge in front.
Kenin showed great character to force a decider and held to love either side of successive breaks to gain an advantage she did not relinquish, staving off a break point to take a 5-1 lead before serving out the match.
Karolina Muchova and Magda Linette will battle it out for glory at the Korea Open on Sunday.
Muchova defeated Wang Yafan 7-6 (7-5) 6-4 after coming from a break down in the first set, while Linette saved four set points before sealing a 7-6 (7-5) 7-6 (9-7) win over Ekaterina Alexandrova with her fourth match point.