Davies, the 47-year-old former world No 1, claimed her fifth title on the Ladies' European Tour this season when she birdied the first play-off hole to beat Thailand's Nantaya Sriswang, South African Tandi Cunningham and Sweden's Louise Friberg. They had all finished on three under par.
Davies' win means she still has a chance of topping this year's European Order of Merit - although she will have to win the Omega Dubai Ladies' Masters next month in order to overhaul South African Lee-Anne Pace.
Davies closed with a 70 to earn her place in the play-off and a birdie at the par five 18th - the first hole in extra time - secured the win. "It's great to keep the Order of Merit going until Dubai," she said. "I know I have to win, but at least I have a chance."
A great final 69 lifted Laing into a tie for 27th on five over par. She remains at No 8 on the money list with over 100,000.