Davies, who had started the day in a five-way tie for sixth, to edged Thailand's Nontaya Srisawang, overnight leader Tandi Cuningham, of South Africa, and Sweden's Louise Friberg.
Davies started well as she birdied the first and went on to complete the round which included a further birdie and an eagle as well as two bogeys with a two-under-par 70 to tie on 213 with the three other women.
France's Cassandra Kirkland finished fifth on 214 while the defending champion, Pormanong Phatlum of Thailand, was joint-sixth with Veronica Zorzi of Italy.
In the play-off, Davies was on the par-5 18th for two and two-putted for a birdie that gave her the title.
It was also the same hole that resurrected her round during regulation play when she eagled to keep her title hopes alive.
Nontaya was on in three and two-putted for a par while the two other players, Cuningham and Friberg, hit their balls into the water.
Davies said: "I love the 18th. It gave me life, it gave me money and it gave me the title. I'll remember this hole for a long, long time. It was my third win in 15 play-offs."
Davies is just over 27,565 short of Lee-Ann Pace's earning on the Henderson Money List and will take the fight to the Omega Dubai Ladies Masters from 8-11 December with Pace finishing joint 15th here.
"This means I have to win in Dubai to surpass Lee-Anne's earnings," she added.
Vikki Laing closed with a 69 to finish leading Scot on 221, a shot ahead of Carly Booth (74), with Kylie Walker two shots further back after she signed off with 78.