Ciganda entered the final round of the Korea LPGA Championship at Sky 72 in Incheon at eight-under par, five strokes behind the overnight leader Lee.
But the 26-year-old overcame the deficit with a furious charge featuring six birdies and ended the regulation tied with Lee at 10-under 278.
They returned to the 18th hole for the playoff, where Ciganda defeated Lee, the world number 44, with a birdie on the first extra hole.
It was the first LPGA Tour title for Ciganda, the world number 37 who made her debut in 2012.
She became the third European winner this year following Sweden's Anna Nordqvist and Germany's Caroline Masson.
Feng Shanshan from China and South Korea's Kim Min-Sun took the third spot on 280.
Feng has performed strongly since winning a bronze medal in Rio. Her third place on Sunday marked her fourth consecutive top-four finish since then.