One of those was Wessberg. She was tied for 19th at the start of her round, but recorded her fourth birdie of the day at the 18th to compensate for a double-bogey 6 at the 13th.
Sorenstam bogeyed four holes on the outward nine but made a good recovery.
"I was just trying to be smart, hit fairways and greens and go from there," Sorenstam said. "I believe I shot level-par the last 10 or 11 holes. I'll take that any time in a championship like this. I just didn't get off to a good start."
Ochoa punctuated her solid round with some spectacular play.
She sank a 30-foot birdie putt at the third and just missed a 60-foot eagle at the fifth. The ball rolled up one slope and down another to creep past the rim of the cup and leave her a 1-foot birdie.
She also benefited from a two-shot swing at the 12th, where she holed a 2-foot birdie putt and playing partner Wendy Ward missed a 7-foot putt for bogey.
Starting one shot behind and tied for second, Ward had six bogeys and a double-bogey 7 at the 17th, where she needed four shots to reach the green. She finished with an 80 for a share of seventh at 2-over 221.
While most players were shooting high 70s or into the 80s in the strong wind, Stacy Prammanasudh shot a 1-under 72. The American had three birdies and moved up from 52nd to a tie for 12th at 3-over 222.
Juli Inkster has had three wildly erratic rounds. The seven-time major winner threatened for the lead during a second-round 68, which was an 11-shot improvement on her opening 79. Her third-round 82 was a 14-stroke swing the other way as she finished tied for 51st at 10-over 229.
Lotta Wahlin of Sweden justified her decision to walk off the course in near darkness after 16 holes on Friday and continue her round just after dawn on Saturday. She birdied the 17th and finished at 5 under to just make the cut. After a short break, she was back on the first tee and finished at 78 for a 229.