Dorothy Delasin, who won this event the past two years, made a strong run at the end with a final-round 67. She finished three shots off the pace at 11- under-par 205 with Grace Park (67).
Kim finished the second round one stroke behind Robbins, who managed to hold off a Saturday charge by the 5-foot-1 Korean. On Sunday, Kim's challenge was too much as she put together a bogey-free round to overtake Robbins at Squaw Creek Country Club.
Kim tallied her first birdie of the day at the par-4 third. She knocked her 5-iron inside six feet to reach 12-under but Robbins held her ground with some solid play of her own.
Robbins, in search of her first win since 1999, birdied the fifth and hit a 9-iron to 12 feet for birdie at the ninth to make a turn at minus-14. She held a two-shot edge over Kim until both players stepped onto the par-4 11th, where the momentum shifted.
Kim hit a brilliant second shot within two feet of the hole to set up birdie while Robbins found the sand with her approach. Robbins blasted out of the bunker but failed to save par from six feet. Kim converted her short putt for the birdie and the duo was tied at 13-under.
Both players were shoulder-to-shoulder until the deciding par-4 17th. Kim hit another remarkable approach and watched as the ball stopped four feet from the cup. The diminutive 25-year-old drained the putt to take the outright lead and never looked back.
'I was nervous because I missed a lot of putts before 17,' said Kim. 'Every time my putts were a double-break. Seventeen was a double-break too. So, I was just a little bit nervous.'
At the closing hole, Robbins missed the green with her second shot but gave a valiant effort with her third. She chipped from off the green and nearly made birdie, then tapped in for par and a one-under 71.
Kim put the finishing touches on a two-putt par to secure the win and the $150,000 first prize.
'I hit it very strong,' Kim said of her first putt on 18. 'I didn't know I was that strong, because I was a little bit nervous. The green was a little bumpy because a lot of the players had been walking on it.'
Kim won for the first time since the 2000 Safeway LPGA Golf Championship. The victory was her fourth on the LPGA Tour.
For Robbins, a nine-time LPGA Tour winner, her second runner-up finish of the year was bittersweet.
'I just really couldn't get the ball close enough,' said Robbins. 'The greens did get a tad bumpy. We knew that was going to happen again. Any time you can finish second, you feel a little short-sighted. At least I did have a shot coming in at the end.'
Tammie Green, another two-time winner of the Giant Eagle, fired a final-round 65 to finish at 10-under-par 206. She was joined by first-round co-leader Beth Bader and tour rookie Natalie Gulbis.
Michele Redman and Pat Hurst tied for eighth at nine-under 207.
Full field scores from the Giant Eagle LPGA Classic