The 25-year-old from Pamplona headed into the final round with a two-shot lead and having not dropped a shot all week at Aviara Golf Club, but three bogeys - offset by only one birdie - meant she had to settle for a two-over 74.
That allowed Kim to join her on the nine-under mark despite a back nine which featured four bogeys - including three straight from the 11th hole. She signed for a 71.
The pair could not be separated when they replayed the 18th for the first time in the play-off, both three-putting. But, on the second occasion, Recari sank an 18-foot putt for birdie to secure her second LPGA Tour title.
Recari had had a six-foot par putt to win the tournament in regulation on the 18th hole, but missed.
Thailand's Pornanong Phatlum (68) and American pair Mo Martin (69) and Cristie Kerr (71) all missed out by one shot after finishing eight under.
Phatlum would have been in the play-off had she not bogeyed the par-four 18th.
Australia's Karrie Webb failed to seriously threaten for the title despite starting the day in second spot, shooting a round of 74 to finish two shots off the leaders in a tie for sixth.
Americans Jane Park (71) and Lizette Salas (72) were level with Webb on seven under.
Rounding out the top 10 was a group of four on six under - including world number one Stacy Lewis.
American Lewis signed for a one-over 73 in her final round, but did have a share of the lead when she was four under through 10.
Her run-in was not up to scratch, however, as she made double-bogeys at 11 and 18 with another dropped shot at 14 to see her drop off the pace.
Tied for ninth with Lewis were Italy's Giulia Sergas (68), South Korea's Haeji Kang (68) and Spain's Azahara Munoz (71).