Ko, world number one Nelly Korda, defending champion Lilia Vu and overnight leader Shin Ji-yai were all on six-under overall as they made their way through the back nine.
In the end it was New Zealand's Ko who took home the $US1,425,000 ($NZ2,285,300) cheque, the highest amount in the event's 48-year history, capping off a memorable three weeks where she won gold in Paris and was also inducted into the LPGA Hall of Fame.
Ko set the clubhouse target at seven under and after Shin and Korda fell by the wayside, Vu needed a birdie putt to force a playoff. But the American underhit her putt on the 18th to give Ko her third major and her first since 2016.
Overnight leader Shin is nicknamed the 'Final-round Queen' but the South Korean was the first to crack when she lost her outright lead with a three-putt bogey on the par-four third, bringing Vu alongside her at the top.
Korda was on par for four holes while Ko birdied the fourth to put herself within one shot of the leaders, meaning the top four were separated by a single stroke.
However, Korda was on a mission to regain her lead and she sank four birdies over the next six holes to take the outright lead while she also saved par after finding the bunker on the 11th to leave Ko and Shin two shots behind.
But Ko also slowly climbed up to top spot with three birdies before a bogey on the 15th saw all four sharing the lead at six-under overall.
Ko then put the pressure on Vu and Korda when she finished with a birdie on the 18th for a final round of 69 to set the clubhouse target.
Korda's chance of clinching a second major this year went up in smoke when she bogeyed the 17th and made par on the 18th to finish two shots behind Ko, the American rubbing the side of her head in disappointment as she walked off the greens.
After Shin double-bogeyed the 17th, it was up to Vu to force a playoff but her putt fell short and Ko broke down in tears when victory was confirmed.
In her disappointment, Vu also missed her putt for par and had to share second spot with Shin, Korda and China's Yin Ruoning at five under.
Ko's previous best result at the British Open was a tie for third in 2015.
"Winning the gold medal in Paris was almost too good to be true and heading into the weekend I thought how is it possible for me to be in contention for the British Open," Ko told Sky Sport.
"I've had the most Cinderella-type story the last few weeks and this is almost too good to be true.
"Of all the major championships, this one I had the least amount of confidence just because I haven't had as much experience playing on links (courses).
"So to be holding this trophy, I can't believe it."
- additional reporting RNZ
