Swiatek, who cruised through her first three matches in Seoul, looked out of sorts in the opening two sets on Sunday, committing several double faults and sending many shots flying long and wide.
But the world No.2 ironed out the errors and got a handle on her opponent's game, wrapping up victory after more than two and a half hours.
It was the Pole's third trophy of the year, adding to her triumphs at Wimbledon and the Cincinnati Open.
Alexandrova, who won the Korea Open in 2022, took advantage of her opponent's early struggles and broke serve three times in the opening set to put herself in the driving seat.
The pair traded breaks early in the second set and Alexandrova continued to pile the pressure on Swiatek, finding herself just a couple of points away from victory after taking a 30-15 lead at 6-5.
Despite having her opponent on the ropes, however, the Russian could not finish her off, and Swiatek took the set into a tiebreaker, where she raced to a 3-0 lead and held on to it to force a decider.
There was another twist in a high-quality third set as Swiatek served three double faults in one game to gift Alexandrova a break, but she quickly brought the set back on serve and dialled up the intensity.
A deflated-looking Alexandrova could only watch as six-time grand slam champion Swiatek hit a pinpoint forehand winner to snatch victory and complete her comeback.
