Korda held her nerve during a chaotic chase for medals and a one-hour storm delay at the end, calmly taking two putts from just inside 30 feet for a one-shot victory.
The 23-year-old Korda gave the Americans a sweep of gold medals in golf. Xander Schauffele won the men's competition Sunday.
Jessica Korda, Nelly's 28-year-old sister who posted a 64 for the low score of the final round, ran out to the green, and the sisters hugged and shimmied in celebration.
Nelly is the first player, man or woman, to win a major and the Olympic gold medal in the same year. She also won the KPMG Women's PGA Championship in June and has won three of the past four individual tournaments.
"This is just kind of like almost legend status as a golfer, period, male or female," Jessica said. "It's tough to win out here and she makes it look easy, but those girls are good. So for her to be doing, it's insane to me. This is like total GOAT (Greatest Of All Time) status to me."
Mone Inami of Japan delivered the host nation a silver medal, and it was nearly better than that.
Inami, given the honor of the opening tee shot on Wednesday, ran off five birdies in a six-hole stretch toward the end, the last one from 8 feet on the 17th hole to tie for the lead. But her approach to the 18th plugged in the sand on the slope of a bunker. The best she could do was to blast out to 30 feet, and she made bogey for a 65.
Lydia Ko of New Zealand had a 35-foot birdie putt to tie for the lead on the 18th. She left it 4 feet short and had to make that for a 65 to finish one behind.
In the playoff for the silver, Ko found a bunker off the tee on the 18th hole, had to lay up and missed a 10-foot par putt.
Ko had to settle for the bronze, after winning the silver in 2016 at Rio de Janeiro. She is the only golfer to win medals in both Olympics since golf returned after a 112-year absence.
There was nothing easy about this final round for Korda, even starting with a three-shot lead. She fell into a tie for the lead, rebuilt it to three shots early on the back nine and then closed with six pars as three players made a bold run at her.
That list include Aditi Ashok of India, at an extreme disadvantage all week with her lack of distance off the tee, some of that brought on by a bout with COVID-19 this summer. With her magic touch on the greens, Ashok stayed in the mix all day.
Her 12-foot birdie putt to keep pace with Ko burned the edge of the cup on the 17th hole, and she had a 25-foot birdie putt on the 18th to stay in medal contention. That slid by the hole.
Korda finished at 17-under 267 and made two double bogeys this week.
One came on the 18th hole of the second round when she needed a birdie for a 59. Korda and her caddie did not realize the tee box was 30 yards forward, leading to the wrong play into the rough behind a tree.
The other was Saturday on the par-3 seventh when her tee shot went left into a collection area. It took Korda three chips to get onto the green, and the double bogey dropped her into a tie with Ko and Ashok.
All three birdied the par-5 eighth -- Korda with a 25-foot putt that was as big as any -- and Korda ran off birdies at the next two holes to restore her three-shot lead.
Inami, Ko and Ashok all whittled away until they ran out of holes and Korda was left with a gold medal, along with a future that never looked brighter.
The Associated Press contributed to this report.