The 15-year-old went into the final round leading by a stroke but pulled clear of the 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.
Catriona Matthew was the leading Briton as a closing 71 left her tied in 11th place on four under par but the day was all about Ko, who moved from South Korea to New Zealand aged just five and now plays as a Kiwi. She was the only amateur to make the cut and succeeds the American Lexi Thompson, who was 16 when she captured the Navistar Classic title last September, as the youngest LPGA Tour winner.
Ko was 15 years, four months and three days old as she wrapped up her stunning success.
Yani Tseng, the world No.1, who led after the first round but then went backwards with rounds of 75, 74 and 74, is already a big admirer of the teenager.
"I'm very impressed. Especially as she's only 15 years old," the South Korean 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."
Stacy Lewis, the world No.2 who was just a shot off the pace at the start of the day and partnered Ko on the final round, tied for sixth. She watched in awe as Ko handled the pressure superbly.
"I was most impressed with her demeanour," said Lewis. "You would have never known that it was the final round of an LPGA event. She played like she had been there before. It was an impressive round for an LPGA pro, let alone a 15-year-old.
"She held it together out there and I was just trying to talk to her at the end, ask her what she's doing next week and kind of keep her distracted a little bit. I think you finally saw some nerves there at the end. I think she finally realised what was going to happen.
"So I was just [asking], 'What are you doing next week? Is your mom here?', and just kind of asking her basic questions. And she thanked me afterwards, but it was an honour just to get to watch her, so I had to say 'thank you' to her."
Inbee Park finished in second place but took the first prize because, as an amateur, Ko was not eligible to receive the cheque.
"It feels great," Park said. "I finished second and get the first-place money. It hasn't happened maybe in 40 years. It hasn't happened that often. And I was lucky this week, I guess."
Ko said: "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."
She insisted her goal of going to college in the United States before turning professional remains.
"I don't think any of my plans will change," Ko said.
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