The amateur had five birdies against a lone bogey at Kumamoto Airport Country Club to finish at 11-under 205, one stroke ahead of South Korean Lee Bo-mee.
"I never thought I would be able to win," Katsu said. "I want to thank the fans who supported me and of course my parents."
Katsu held a two-stroke lead heading to the par-5 18th. Her third shot found the greenside bunker but she chipped out to eight feet and made the par putt.
Her victory was secured when Lee's third shot on 18 landed 10 feet from the hole.
South Korean Kim Hyo-joo was the previous youngest winner in Japan when she captured the Suntory Ladies Open in 2012 at the age of 16.
Katsu, a first-year student at Kagoshima High School, started the final round tied for second, one stroke behind Mami Fukuda who shot a 66 on Saturday to top the leaderboard.