Ko was the only player in the last three groups to not collapse out of contention, carding a one-under-par 71 to edge German Esther Henseleit into second, with China's Lin Xiyu taking bronze.
"Going into this week, everyone was saying, 'Oh, what if you finish and collect the gold on top of the silver and bronze you have'," Ko said.
"Of course I wanted to do that, complete it, too, but it's much easier said than done."
The former world number one was cruising to the title, leading by five shots with six holes to spare before hitting an iron shot on the par-four 13th into the water and making a double-bogey.
Henseleit took advantage, finishing with back-to-back birdies to sign for a closing six-under-par 66 and post an eight-under total in the clubhouse.
But Ko held her nerve, reeling off four successive pars before securing gold in style with a birdie on the par-five 18th hole, ending the tournament on 10-under overall.
The 27-year-old was already the first golfer to win multiple individual Olympic medals and now has more in total than any other player in history.
Americans Chandler Egan, Burt McKinnie and Francis Newton took individual and men's team medals in the 1904 Olympics in St Louis.
Ko was runner-up behind Park In-bee when golf returned to the Olympics from a 112-year absence in Rio in 2016, before finishing third in Tokyo three years ago.
She kept her rivals at arm's length once she first reached 10-under with a 45-foot birdie putt on the seventh.
"That was crucial, and I think when those kind of moments happen, that's when you know that, hey, it could potentially go your way," added Ko.
World number 54 Henseleit had been nine shots off the lead at the halfway stage of the event and seven back going into Saturday.
Her silver medal continues a breakthrough season which has seen the 25-year-old post top-15 finishes at three major championships to climb the rankings.
Lin outshone her more fancied compatriot Yin Ruoning with a three-under 69 to become the second Chinese golf medallist after Shanshan Feng also won bronze in 2016.
A group of four players finished in an agonising tie for fourth, one shot outside a possible bronze medal play-off, after Lin made birdie on the final green.
The Philippines' Bianca Pagdanganan, Australian Hannah Green, South Korea's PGA Championship winner Amy Yang and Miyu Yamashita of Japan narrowly missed out on the podium.
Korda falls away
Reigning champion Nelly Korda was in medal contention when Ko slipped up at the 13th, sitting just four strokes off the lead.
But the world number one hit a dreadful approach shot into the 15th green, coming up 50 yards short of clearing the water before racking up a triple bogey.
"I just shanked it," she said. "I just hit it fat and hit it short and into the water."
Korda ended with a three-over 75, finishing tied-22nd.
Home favourite Celine Boutier was given a rousing reception on the first tee and cheered on by thousands of fans across the course as she attempted to win France's first Olympic golf medal.
But the seventh-ranked Frenchwoman stumbled to a two-over 74.
Boutier and Korda were not the only hopefuls to fall away on the final day.
Overnight co-leader Morgane Metraux of Switzerland suffered a triple-bogey meltdown on the fifth hole en route to a 79, while Rose Zhang also struggled in the last group and was four over par on the front nine.
The other two players who were within four shots of the lead heading into the fourth round, Atthaya Thitikul and Mariajo Uribe, also both quickly dropped down the leaderboard.
