It was the second title of the season for Alexandrova, who is ranked 24th in the world and was seeded second in the WTA 250 event in Seoul.
Alexandrova was forced to play catch-up for most of the opening set against the aggressive play from the former French Open champion.
But with superior court coverage and better control on unforced errors, the Russian rallied from a breakdown three times and also saved a set point to force a tiebreaker which she edged to take the opening set.
Ostapenko, who won the Korea Open title and her maiden Grand Slam trophy at Roland Garros in 2017, suffered a right foot injury during the second set and needed a medical timeout to receive treatment on court.
The Latvian could not muster much of a fight after the injury as Alexandrova breezed through the set and sealed the match with a backhand return winner, her 27th of the match.
