Johnson, a rookie who has finished no better than 12th in any of her previous nine starts this year, played late in the afternoon and grabbed the lead away from 16-year-old Lexi Thompson.
Thompson, who will be allowed to go through the LPGA Tour's qualifying tournaments later this year even though she is under the circuit's age limit of 18, shot a 66 over the Senator Course on the Robert Trent Jones Golf Trail.
Johnson then came through with a 65. She played the final 10 holes in 7-under and birdied both the 17th and 18th.
Defending champion Katherine Hull shot a 70 and was tied for 18th.