The Surrey player had forced her way into the extra-time decider with two birdies in the final four holes in a closing 69 for a two-over-par 286. She looked set to take the title when she had a five foot birdie putt at the first play-off hole.
But Davies, who won the McDonald's Championship of Europe at Gleneagles in a play-off last month, missed the chance, and then took a bogey six at the same par-five 18th at the second time of asking to open the door for Mendiburu to claim the title with a par.
Germany's Elisabeth Esterl, who dropped out at the first play-off hole, and Spain's Raquel Carriedo, who matched Davies' six the second time around, also had to settle for second best as Mendiburu claimed victory.
For Davies, who had been less than complimentary about the course earlier in the week, it was a third second place to set beside her three wins this summer. The pounds 7,516 prize lifted her season's total to pounds 204,521 at the head of the money list.Reuse content