Sung Hyun Park, overnight leader Michelle Wie and Ko, the final group of the day, were within a wedge shot into 18 when play was suspended for lightning.
But they couldn't catch Inbee - Sung Hyun Park was at four-under on the day and 16-under for the tournament, while Wie was even-par on Sunday and sitting five strokes behind.
Canadian Brooke Henderson shot 66 to finish five behind Inbee.
Minjee Lee was the leading Australian, tied 30th at six under after a closing 73, with Su Oh (66) and Karrie Webb finishing fast to tie for 48th at one under.
Inbee reeled off eight birdies up to the 17th hole, draining a series of long putts in a near-flawless display on the greens.
"My putting was amazing today, obviously," she said. "I couldn't make any putts yesterday and, obviously, I made up for it today.
"Pretty much everything I looked at, it wanted to drop in. It was very consistent ball striking all week and, obviously, there is a lot of birdie opportunities out there and I was able to convert the birdies. This was one of my best putting days ... I was just in that zone."
Despite seven majors, Inbee said she surprised herself by winning so soon. The 28-year-old took six months off shortly after winning Rio Olympic gold to recover from a thumb injury and was playing only her second event.
"I thought it may take maybe a couple months to kind of get back out on the tour and to get my rhythm back," she said.
Wie had been two in front after birdies on the second and third holes before her round unravelled when she four-putted for a double-bogey on the par-5 fifth.
"Overall, I can't complain but, right now, it stings a little bit," Wie said. "Just a couple of putts didn't go in, and Inbee played really well.
The American finished alongside Henderson and last year's Singapore champion Jang Ha-na (69).
- AAP
