The 15-year-old went into the final round leading by a solitary stroke but pulled clear of South Korean Chella Choi with four straight birdies on holes 10 to 13 and signed for a five-under-par 67.
Ko was left relieved when Choi bogeyed the 17th, having picked up a stroke at the 15th hole to close within three.
After parring that hole herself, the youngster held her nerve to finish three shots clear on 13-under 275 despite bogeying the 18th.
Ko said of her victory: "It's great to win, and the last few holes, it got a bit nerve-wracking, but Stacy Lewis after my birdie on 15 said, 'You know, you can do it', and it was really great to have another player that I look up to giving me that much support. So it was really awesome."
She insisted her goal of going to college in the United States before turning professional will not be affected.
"I don't think any of my plans will change," Ko said. "I'll still remain an amateur and then finish high school and then go to college in the States."
Ko, who moved from South Korea to New Zealand aged just five and now plays as a Kiwi, was the only amateur to make the midway cut and takes over from American Lexi Thompson as the youngest LPGA Tour winner.
Thompson was 16 when she captured the Navistar Classic title last September.
Ko was 15 years, four months and three days old as she wrapped up her stunning success.
World number one Yani Tseng, who led after the first round but then went backwards with rounds of 75, 74 and 74, is already a major admirer of the teenager.
"I'm very impressed. Especially as she's only 15 years old," South Korean Tseng said.
"I didn't even know what I was doing when I was 15. So it's pretty amazing to see her play this good in the best stage.
"It's good to see so many younger players now on the tour, and it's good to see the young generations coming out.
"It's good for the game. I feel I'm old on the tour now. I'm only 23, but there's so many younger players now."
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