Ko won the silver medal at Rio 2016 before picking up bronze in Tokyo three years ago, but her victory in Paris also pushed her career total to 27 points required for a place in the LPGA Hall of Fame.
She was the joint leader going into the final day and built a five-shot lead on the back nine to put herself out of reach as her competitors dropped away, though she set up a nervy finish as she carded a one-under 71.
Germany's Esther Henseleit almost caught her as she hit a six-under 66 to shoot up the leaderboard to finish on eight under, coming out of nowhere to clinch the silver medal.
Xiyu Lin was almost forced into a play-off for bronze, but she birdied the final hole for a 69 to finish on seven under, one stroke ahead of fourth place.
Switzerland's Morgane Metraux had been Ko's co-leader at the start of the day, but it was a day to forget as her game collapsed, and she finished the event in 18th.
Nelly Korda and Rose Zhang also struggled to maintain their momentum on Saturday, as Ko surged out of their sights on the leaderboard.
The world number one golfer emerged triumphant from a fierce battle in the final round, winning by a single stroke from Japan's Mone Inami and New Zealand's Lydia Ko.
Inami fired a 65 and was the co-leader at 17 under until she bogeyed the last, finding a greenside bunker with her approach and failing to put the ball close, then missing her 20-foot par putt.
That meant Korda walked down the 18th knowing she was in pole position to take gold, albeit needing to keep an eye on Ko.
Both Korda and Ko found the green safely, each with an outside chance of birdie. Neither could sink that first putt, but Korda left herself a tap-in for the title and made no mistake.
The 23-year-old then was embraced by her sister Jessica, dancing across the green to offer a fond embrace.
Jessica Korda had fired a joint best-of-the-day 64 to finish in a tie for 15th, but it was Nelly's day to triumph.
The champion set herself up for this success with a 62 in round two, and consecutive rounds of 69 on Friday and Saturday took her over the winning line.
Play was briefly suspended with two holes left to complete for the front-runners, as the nearby storm caused a 49-minute delay just while the tension was ramping up.
But fears of a Saturday washout were allayed to ensure the tournament went the distance, and with gold on 17 under going to Korda, Inami took silver in a play-off when Ko bogeyed 18, the first extra hole.
Inami and Ko, who also made 65 in the final round, had finished tied on 16 under, one ahead of India's Aditi Ashok, whose closing 68 was not enough for a medal.
Korda's triumph meant the USA achieved a golf double, with Xander Schauffele having won the men's title.
