'This is something that, as a golfer, you dream of happening,' said Stupples. 'But for me, I was never really sure if I could do it.'
Jung Yeon Lee, who matched the 18-hole tournament record with a 60 in the opening round, was joined by Grace Park in a tie for second at 17-under-par 263.
Stacy Prammanasudh posted a 67 to finish alone in fourth place at 15-under-par 265. Laura Davies, Aree Song and Shi Hyun Ahn were two shots further back at 13-under-par 267.
Stupples held a one-shot edge to start the final round but stumbled out of the gate with a bogey on the opening hole of the Dell Urich layout.
The 30-year-old buckled down quickly and recovered with a birdie at the second. Stupples then two-putted for a birdie at the par-5 third and added a birdie at the par-5 sixth to reach 17-under.
Stupples dropped her approach inside six feet for a birdie at the eighth and ran home a 12-foot putt for a birdie at the 10th.
At the par-5 13th, Stupples hit her second shot within 30 feet and drained the eagle putt to pull three shots clear of the field at 21-under par.
Stupples padded her advantage with a birdie at the 16th and parred the two remaining holes for the win.
'I knew where I was all day,' said Stupples, who collected $225,000 at the season-opening event. 'I like the challenge of Grace and Jung Yeon Lee there for a bit, and I really liked that because it's all about the challenge. That's what golf is all about.'
Park kept pace with Stupples early on thanks to a solid front nine. She tallied a birdie at the third and picked up back-to-back birdies from the fifth to move to minus-17.
The Korean then knocked her approach inside 18 feet at the 10th and converted the birdie putt.
Things cooled down for Park from that point on, however, and the 25-year-old closed with a bogey at the last to join Lee in a tie for second.
'Obviously, it's disappointing the way I finished, but Karen was awesome,' said Park. 'She didn't make a single mistake from the outside, and I couldn't hang in there.'
Se Ri Pak, Mi Hyun Kim and Seol-An Jeon shared eighth place at 12-under-par 268. Pat Hurst followed at 11-under-par 269.
Becky Morgan and Eva Dahllof tied for 12th place at 9-under-par 271.