The Swede made seven birdies and two bogeys and went around on 67 strokes, five under par, and is in the same place as the South Korean Chun In-Gee.
Leads make the American Nelly Korda in one fell swoop smaller.
Golf major ANA Inspiration started in 36-37 degrees heat, however, the players did not get affected by fire smoke from the many forest fires in California.
Linnea Ström on par
The next Swede in the results list is Anna Nordqvist who went around on 70 strokes, two under par, after a double bogey and four birdies.
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Linnea Ström went on par, 72 strokes, while Pernilla Lindberg as well as Caroline Hedwall ended up on 76 strokes, four over par.
Daniella Holmqvist had a nightmare hole, the sixth, where she did a quadruple bogey.
In total, it was 80 strokes for her.
ANA Inspiration is usually played in the spring, but was moved due to the corona pandemic.
This makes the conditions on the course different, with a thicker grass and a different feeling on the greens.