Lewis found trouble in the left rough and was unable to save par leaving Ko with a short putt to win the title for a third time, the first time as a professional having won back-to-back in 2012-13 as an amateur.
"It's been such an amazing week. I made some really good up and downs on the front nine but I just couldn't get anything going and I wasn't hitting anything close," Ko told reporters.
"Obviously Stacy played awesome and so did the other girls so I knew I needed to play consistent and that's what I tried to do."
Defending champion Ryu set the early pressure with a scintillating bogey-free 64 to finish at 11-under, tied third with fellow Korean Kim Sei-young (68) before Lewis one upped her.
Ko birdied the third hole but bogeyed the ninth before grinding out nine successive pars.
The 18-year-old had a 10-foot birdie chance on the 17th hole to take the lead after a lucky bounce out of the rough but missed on the high side.
After her approach to 18 finished a long way from the hole she faced a nervous two-putt to make extra holes but almost drained the monster putt for the win.
A similar lag in sudden death was enough when Lewis missed her 10-foot par save.
Canadian teenager Brooke Henderson, fresh off her maiden LPGA win, finished at four under in a tie for 23rd in her quest to be the first Canadian winner since Jocelyne Bourassa won the inaugural event in 1973.
(Reporting by Ben Everill in Los Angeles; Editing by Greg Stutchbury)
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