'The swing started getting a little iffy at the end, but fortunately my putter was real hot,' said Steinhauer, who collected $195,000 for eighth LPGA Tour victory. 'Got me out of a lot of trouble.'
Steinhauer shot a 5-under 67 on Sunday to finish the victory at 17-under- par 271. Kim birdied the last three holes, including two from off the green at 17 and 18, for a 6-under 66 to lose by a stroke.
Annika Sorenstam, the 2006 champion, also shot a 67 in the final round, but came up three back at minus-14. Rachel Hetherington joined Sorenstam after a 69 tied her with the Swede, who is nearly recovered from her back and neck injuries.
'This week has been the best of the year I would say,' acknowledged Sorenstam. 'I'm feeling better every day. I think overall I have a lot of positive things to take from this week.'
The tournament came down to the final three holes as balls were flying into holes from everywhere.
Kim and Sorenstam both birdied the par-5 16th to get within one of Steinhauer, but both missed the green at the par-3 17th. Sorenstam came up right and short, while Kim landed left of the putting surface.
Sorenstam could only manage par, but Kim chipped in to tie for the lead at minus-15. Steinhauer landed in a bunker at the 16th with her third and only blasted out to 20 feet. She made that putt to move back ahead by a stroke.
Kim split the fairway at the tough closing hole at Panther Creek Country Club and her second stopped in the left fringe, 25 feet from the stick. Kim drained that birdie putt from off the green to tie for the lead again, but Steinhauer rolled in a 28-foot birdie putt of her own at the 17th to get back in front.
With Kim watching from behind the green, Steinhauer drove into the fairway. Her approach barely cleared the water and nestled in a bunker. Much like her sand play at the 16th, Steinhauer hit a bad shot that rolled 25 feet away into the rough.
Steinhauer needed to hole the putt for the win or get up and down to force a playoff. She snaked in the long par save for her first win since last year's Women's British Open.
'I was in between clubs,' said Steinhauer, referring to her awful approach at 18. 'I didn't make a positive swing. I didn't trust it. I ended up in the bunker and it was a poor shot.'
Kim added to the drama with her play late and may have sent a message to American Solheim Cup captain Betsy King. Last week, King passed over Kim with her captains' picks and Kim was aware this week.
'It was incredible. I was just going,' said Kim. 'These are points for the next Solheim Cup. It was so much fun.'
Angela Park shot a 4-under 68 and finished alone in fifth place at minus-12. Jeong Jang fired a 7-under 65 and took sixth at 11-under-par 277.
Joo Mi Kim (69) and Michele Redman (72) tied for seventh at minus-10.