The win broke a 12-year stranglehold that foreigners had on the crown. The last American winner of this tournament was Patty Sheehan in 1993.
'It feels great. It has been a long time,' said Inkster, who won for the first time since the 2003 Evian Masters. 'I've worked really hard this winter and its great to see my hard work pay off.'
Inkster broke through despite cold, rain and fading sunlight. Due to a one hour, 50-minute rain delay, portable lights were brought out to help illuminate the final two holes.
Third-round leader Sarah Lee struggled to a final-round, 1-over 73 to end two shots back at 13-under-par 275. Lee was looking for her first tour win, but settled for her fourth second-place finish in her five-year career.
Aree Song, who led after the second round, also shot 73 to end at minus-12. Cristie Kerr and Catriona Matthew each posted rounds of 3-under 69 to share fourth place at 11-under-par 277. They were joined there by reigning Women's British Open champion Jeong Jang (70).
Lee and Song were for the lead most of the round. Lee birdied the first and second to get to 16 under. Song also birdied the second to trail by two.
Both Song and Lee bogeyed the fourth. Song birdied No. 7 to get back to 14- under and Lee joined her there after a bogey at the eighth.
Inkster, meanwhile, dropped in back-to-back birdies from the fourth to get to 12-under. From there, she parred her next five holes around the turn.
The 45-year-old rolled in a birdie on the 11th, then sank a 4-footer for birdie on 12 to join Lee and Song in the lead at minus-14. Lee answered with a birdie at the 12th to regain a one-stroke lead.
Lee made it two in a row as she birdied 13 to go two clear. Inkster, playing one group ahead of Lee and Song, dropped her approach shot five feet from the cup at the 14th.
Inkster sank that birdie putt to move to 15 under. Lee found a transition area off the tee at 14. After her second shot plugged in a bunker, Lee blasted across the green.
She could do no better than double bogey, which dropped her to minus-14, one behind Inkster. Song found two bunkers on the 14th en route to her own double bogey that put her out of the running at minus-12.
Lee parred 15 and 16, while Inkster missed the green at the 16th and could not save par. So Lee and Inkster were tied at 14 under. Lee fell one back as she bogeyed the 17th after missing the green long and right.
Inkster, going for her 31st tour win, pitched her third to 3 feet and sank the birdie putt on the par-5 closing hole to get to 15 under.
'I hit the ball very well today,' said Inkster, who claimed $210,000 for the win. 'I think I only missed one green and that was on 16. I had a lot of opportunities for birdie. I just stayed patient all week and tried to keep hitting good shots.'
Lee, needing eagle to force a playoff, could only par the last despite her eagle chip running just past the lip of the cup.
'I made birdie on 12 and 13 and I was in good position,' said Lee. 'On 14, I was into the wind so I grabbed my driver and swung aggressively. I just pulled it. The second shot off the rocks was really difficult, I didn't know how the ball would come off them. I did imagine the shot before I hit it, but it didn't work.'
Women's world No. 1 and three-time champion Annika Sorenstam tried to make a miraculous comeback on Sunday. She trailed by 13 strokes entering the round, but fired 6-under 66 to fly up the leaderboard.
Sorenstam ended at 7-under-par 281 and in a tie for 19th place on the Prospector Course at Superstition Mountain Golf and Country Club.
Young-A Yang (69) and Paula Creamer (70) shared seventh place at 10-under-par 278. Candy Hannemann, Patricia Meunier-Lebouc and Stacy Prammanasudh were one stroke further back at minus-9.