Defending champion Annika Sorenstam fired a bogey-free 66 to share third place. She was joined there by Juli Inkster. Reigning Women's British Open champion Karen Stupples is one stroke further back at minus-5.
Ochoa began her day on the 10th hole of the Prospector Course at Superstition Mountain Golf and Country Club. She promptly drained a 12-foot birdie putt to quickly move into red figures.
The Mexican dropped her second shot 8 feet from the cup at the next and rolled the putt in for her second birdie. Ochoa converted another birdie try at 12th.
Ochoa capped a run of four straight birdies by kicking in a 4-foot birdie putt at the 13th. After a bogey at the 16th, the 23-year-old sank an 8-footer for birdie on No. 17.
She came right back with a birdie on 18 to make the turn at minus-5. Ochoa two-putted for birdie at the par-5 second. She then joined Lim in the lead with a 6-foot birdie putt at the seventh. Ochoa parred her final two holes to remain tied for the lead.
'It was the first time I made four birdies in a row at the start. So I was very excited,' Ochoa said. 'I thought I would just go low today and take advantage of the opportunities.'
After five straight pars to start her round, Lim rolled in a 22-foot birdie putt at the par-4 sixth to get into red figures. The Malaysian made it two straight when her 6-foot birdie try at seven found the bottom of the cup.
Lim then drained a 28-foot birdie try at eight and a 2-foot birdie putt at nine to make the turn at minus-4. The 30-year-old three-putted for bogey at the 14th, but bounced right back with a birdie on No. 15.
The South Carolina alum sank a 7-foot birdie putt at 16 and a 23-footer at 17 to move to 6 under. Lim capped her second run of four straight birdies as her 6-foot birdie putt at the last fell to give her a piece of the lead.
'It was a little slow this morning when I first started,' said Lim, who posted a career-best round. 'I kind of missed a couple of greens the first few holes, made up and downs, and once I started getting a little more comfortable, I hit a green and then started making some birdies.'
Sorenstam, the 2001 and 2004 champion of this event, began on the back nine and picked up her first birdie at the 13th. She went on to chip in for birdie at the 15th.
Around the turn, the Swede birdied the second and drained a 25-foot birdie putt at five to get to 4 under. Sorenstam converted back-to-back birdie putts from the seventh to get within one stroke of the leaders.
'I'm very pleased with the way I played today,' Sorenstam said. 'I thought I hit a lot of good quality shots.'
Sung Ah Yim, Soo-Yun Kang and Moira Dunn share sixth place at 4-under-par 68. Candie Kung, Karrie Webb, Kim Williams, Dawn Coe-Jones, Paula Creamer, Beth Daniel, Natalie Gulbis and Marcy Hart were one stroke further back at minus-3.