The 23-year-old carded a four-under-par round of 69 at Royal Pines to finish the tournament at 16 under.
Local amateur Minjee Lee was two shots back in outright second place after she also managed a 69 on Sunday.
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The 17-year-old fired three consecutive birdies on the front nine to draw level with Woods, but the American closed with three birdies in her final six holes to seal the win.
South African Stacy Lee Bregman and Swede Camilla Lennarth were two shots behind Lee in a tie for third.
South Korean duo Minsun Kim and So Young Lee were tied for fifth on nine under alongside Swede Caroline Hedwall, who rounded off her tournament with a 66 - the joint best final round.
A delighted Woods said after her victory: "This is a huge accomplishment for me.
"The Ladies European Tour has been great to be able to play this last year, I've been able to see all of these great players, play with Solheim Cup members, so I've learned so much from all of these girls and to be able to come out here and actually compete with them and come out on top was huge for me."
The win did not come as too much of a surprise for the Phoenix-born player, even though she missed the cut last week.
"Not necessarily a shock, but I missed the cut last week by two shots in New Zealand - 77, 71 - so I didn't play well last week but I came into this week with a new mindset, I worked on a few things and everything just clicked.
"It worked out really well. After the first round I knew I could win, so from then on that was the goal."