The previous youngest major champion was Morgan Pressel who was six months older than Ko when she won the 2007 Kraft Nabisco Championship.
"To finish with two birdies, finish on the last 72nd hole, with a birdie, it doesn't happen often," Ko was quoted as saying on the LPGA website (www.lpga.com).
"It's definitely one of the top rounds of my whole entire life, and I'm sure it will be in my career."
It was the lowest final round by a winner of a women's major, surpassing the 64 Karen Stupples carded when triumphing at the 2004 British Open.
South Korea's Lee Mi-hyang had begun the day at the head of a packed leaderboard on 10 under, one shot clear of Thompson.
Thompson's challenge faded after she moved three shots ahead of Ko during the front nine.
"I struggled on the back," Thompson said. "I kind of lost my tee ball and didn't hit good iron shots, and it's kind of hard to beat somebody that shoots 63."
World number two Ko fired eight birdies with no dropped shots.
(Reporting by Martyn Herman; editing by Clare Fallon)
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