Ochoa sank a 30-foot birdie putt at the third and nearly claimed an improbable 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 one-foot birdie.
Ochoa also saw her rivals falling by the wayside.
Disastrous round
Starting at five under, Wendy Ward had disastrous round with six bogeys and a double-bogey seven at the 17th where she needed four shots to reach the green.
She finished with an 80 for a share of seventh place on two-over 221. Karine Icher of France, who began the day on three under, bogeyed the first two holes and struggled to a 77 to finish one over.
Local favourite Catriona Matthew, starting at five under, played her second shot into the Swilcan Burn creek to bogey the first hole.
She finished with an 80 for a two-over 221. Defending champion Sherri Steinhauer also dropped out of contention.
The three-time champion started with two bogeys to slide from three under to two-over after the first nine. She eventually made an 80 to finish four-over on 223.
Apart from Ochoa, Stacy Prammanasudh was also one of the few players able to be satisfied with her day after shooting a 72 to rocket up the leader board.
The American had three birdies and moved up from equal 52nd to 13th at three-over 222.
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 five under to just make the cut and after a short break, she was back on the first tee playing with a marker and made a five-over 78 for a 10-over 229.