It was the British player's 15th victory in 10 years on the tour. Davies won four events last season on her way to taking the Player of the Year award.
On the men's tour, Gene Sarazen and Walter Hagen are the only players ever to win four in a row. Hagen won the PGA Championship from 1924-27 while Sarazen took the Miami Open from 1926-30 with no tournament played in 1927.
Robbins, seeking her second win this season and fifth of her six-year career, forced a play-off by rolling in a 10-foot birdie putt on the 18th hole. That capped her round of 69 to tie with Davies, who shot 68 for a 15-under 277 total.
Playing on the 400-yard 18th for the play-off, Davies pulled her tee- shot left on to a walkway, but hit her second shot short of the green and then chipped within three feet.
Robbins drove down the centre of the fairway, but her approach shot from 100 feet went over the green and into a bunker. Her wedge shot landed six feet from the hole, but she pushed her putt past the cup and had to tap in for a bogey five.
It was the first play-off win in seven attempts for Davies, while Robbins had won three of her four titles in sudden death in her six years on the tour.
Last year in this tournament, Davies came from three shots behind to win on the final hole and become the first to win a LPGA tournament three times in succession since Sandra Haynie took the Charity Golf Classic from 1973-75.
Laurie Brower, without a victoy in six years and making the cut for the first time in five attempts this year, finished tied for third place after shooting a 70 with five birdies.
Also at 281 was Barb Mucha, who struggled to a 73 with crucial bogeys on the 10th, 11th and 12th holes after carding a course record-equalling 65 in the first round.Reuse content