At 18 years and nine months, Henderson became the second-youngest woman to win a major after New Zealander Ko, who won last year's Evian Championship aged 18 years and four months.
Henderson, who denied Ko a third consecutive major, is just the second Canadian to win a women's major after Sandra Post (1968 Women's PGA Championship).
Henderson earned her victory in style, closing with a 65 to catch Ko (67) at six-under 278, one stroke ahead of Thailand's Ariya Jutanugarn (66), who was going for a fourth straight victory.
Wielding a hot putter, Henderson rolled in a 90-foot eagle from off the green at the par-five 11th to throw down the gauntlet.
"I had seven yards of fringe to go over and then a big mound so I really focussed on the pace to make sure I had a close birdie putt and it ended up falling in and that was really the momentum changer," Henderson said.
She later holed another monster putt, this time from 40 feet at the 17th, to draw level with Ko.
"It was a pretty good day for me," Henderson said at the victory presentation after collecting her second victory on the LPGA Tour.
"I really didn’t feel a ton of pressure or a ton of nerves, which I think is the key to shooting six-under in the final round and then being able to play a playoff."
Asked whether she had ever dreamed of such a moment, she responded: "Definitely in my dreams. I don’t know if I ever thought it would come true."
Ko was left to rue what would have been an historic hat-trick of major victories. She had been aiming to become the youngest woman to win three consecutive majors.
She did not make a bogey all day, and her only big mistake came at the 17th where she missed a three-foot birdie putt that opened the door to Henderson.
(Reporting by Andrew Both in Cary, North Carolina; Editing by Peter Rutherford)
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