Ko brushed tears from her eyes after the draining the putt, having notched her first win in 44 starts.
She now boasts a 15th LPGA title and two major wins since turning professional in 2014.
"I don't think I've ever cried in the other 14 (wins)," she told reporters at Lake Merced Golf Club with a laugh.
"And I cried like four times in the span of two minutes which is kind of embarrassing.
"Every time I'd see my sister, I'd cry, every time I'd see my mum I cry, Ted (Oh), my coach was crying so then I cried again.
"I'm like 'God, get a hold of yourself!'
"But you know it was emotional because they'd been through it with me, it's not like you're the only one out there.
"That's why it's so meaningful."
Ko led by a stroke ahead of Jessica Korda into the final round but for a period it looked like more disappointment was in store for the young New Zealander.
She made three bogeys in her first six holes to fall two shots adrift of the lead before a stunning rally on the back nine at the San Francisco course where she won back-to-back titles in 2014-15.
She all but won the tournament on the 18th, where she nearly pitched in for an eagle, but made sure of it when she returned to the par-five hole for the playoff.
Her three-wood cleared tree limbs fringeing the fairway before landing a few metres short of the green. It bounced on, rolled and missed the hole by inches.
Ko turned 21 during the week and can now celebrate her triumph at a local bar, having passed the United States' legal drinking age.
"We can officially celebrate with alcohol, champagne and (I'll) remember to take my ID," she said.
(Reporting by Ian Ranson in Melbourne; Editing by Amlan Chakraborty)
