England's Stupples, the 2004 Women's British Open champion, had taken a one-shot lead into the final round at Mission Hills Country Club in Rancho Mirage after rounds of 69, 69 and 68 had left her at ten under par, however a closing round of 78 scuppered her hopes.
Reigning Women's British Open Champion, Scotland's Catriona Matthew, was one over for her final round and one under for the week to claim a tie for 15th.
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Hide AdStupples' demise left Taiwan-born Tseng and Suzann Pettersen of Norway to duel it out for the title after both had started a shot behind the leader following rounds of 67 on Saturday.
Tseng struck the first blow when she chipped in for eagle at the par-five second as both Stupples and Pettersen birdied and she added two more birdies while the Norwegian bogeyed the par-four sixth. Both birdied the par-five 11th and Tseng gave Pettersen hope when she bogeyed the par-four 12th to close the gap to four strokes.
As Tseng parred her way home, Pettersen closed the gap further with a birdie at the 16th but when she pulled her approach shot at the 18th hole wide of the green it left her needing to chip in for eagle to have a hope of forcing a play-off. Pettersen's effort came close but stayed out of the hole and Tseng was left with two putts for victory, sending her lag putt to within inches before tapping in.
Korea's Song-hee Kim took third place at nine under following a 70, while world No 1 Lorena Ochoa was one over for the day to finish in fourth at six under.