South Korea's Se Ri Pak took the title with a four foot birdie putt at the first extra hole.
Davies had overturned a two shot overnight deficit with a final round of 68 which included six birdies. It set a 12 under par 276 target that was eventually matched by Pak (70) and Australia's world No1 Karrie Webb, who holed from four feet for a birdie at the 18th in 68.
At the same 18th in the play-off, Davies saw a 30-foot chip for birdie stop one roll short of going in before Pak stepped up to hole her winning putt.
Davies and Webb, whose share of second place clinched the Order of Merit, Vare Trophy (scoring average) and Player of the Year, both banked just over pounds 65,000.
"It was a shame that it didn't quite come off, but it's still a good way to finish a good year," said the 36-year-old Davies, who finished with three wins in Europe and also won in Japan.
But, for the first time since 1993, she has now finished a season without a victory on the US LPGA Tour.
After bogeys at the fourth and fifth, Davies looked to be slipping out of contention. Then she made six birdies, including three in a row from the 11th, to put herself back in the hunt.
"But I always thought that I needed to get to 13 or 14 under to win, and I was proved right," she added.
Scotland's Janice Moodie, with a 70 that included a best-of-tournament homeward nine of 31, finished in a share of seventh place on six under.
Catriona Matthew and Helen Dobson, the other two British players in the elite, 30-strong field, both shot 74 and finished on 288 and 291.
Sergio Garcia's amazing shot from behind a tree at the United States PGA Championship in August has been named the 1999 Canon Shot of the Year.
Two behind Tiger Woods with three holes to play, the 19-year-old Spaniard smashed at the ball with his eyes shut, then opened them and raced up the fairway to see the ball reach the green.
Named last week as the European tour's Rookie of the Year - he finished third on the Order of Merit - Garcia follows fellow Spaniard Miguel Angel Jimenez as the recipient of the Shot of the Year award. Jimenez chipped in to win the 1999 Lancome Trophy.Reuse content