Smriti, who shot 80 on first day, scored 77 in the second and missed the cut by five shots.
Adachi was taking the lead going into the final round for the first time after the 26-year-old from Kyoto signed out with a 3-under 69 to take a three-shot lead.
Making birdies on the first, third, sixth and three consecutively beginning with the 14th, Adachi said her only blemish was on the greens.
Sitting on tied third are two Chinese Taipei players, Tsai Pei-Ying and Liu Babe, on 145.