The 17-year-old would have been even further ahead after an extraordinary round - which included five birdied in a row from the 10th - had she not finished her round with two bogeys.
Jutanugarn finished 11 under par and three clear of a three-way tie for second shared by Stacy Lewis, Se Ri Pak and Beatriz Recari.
Half-way leader Lewis shot a disappointing 76 - including three bogeys in the last three holes - to slip off the pace.
Jutanugarn was delighted with her play.
"I went to the course today (under) pressure as there were so many fans coming to see me," she said. "Not only my family, but also the entire country has hopes for me. But after I heard their hands clap, it became an inspiration.
"Stacy (Lewis) did not play her best game today and my score was not bad," said Ariya, adding that the pressure of leading will not faze her.
"I have nothing to worry about. I have the game plan and have to focus on it."