Olson, who secured a tied ninth finish at the ANA Inspiration earlier this year, sank four birdies and a superb eagle at the ninth to steer clear of the chasing pack.
"I think the biggest thing that I like about major championships is how it forces you to bring your best game," she said.
"You can't really fake it. You can't get away with poor shots. So I love that. Obviously the atmosphere is a lot of fun. When you're playing well, you just feed off it."
Seven-time LPGA Tour winner Kim Sei-young of South Korea is the nearest challenger lies at 12-under after a spotless 64, while American Mo Martin a further two shots back in third spot on 10-under.
Reigning Women's British Open champion Georgia Hall lost ground after a third consecutive 68, five strokes behind 54-hole leader Olson.
(Reporting by Hardik Vyas in Bengaluru, editing by Pritha Sarkar)
