The pair is knotted at 12-under-par 132 at the Legacy & Independence Courses at Reunion Resort and Club. Ochoa and Davies are three strokes ahead of Natalie Gulbis, who also shot a 66 on Friday.
Mi Hyun Kim, the defending champion, posted a 3-under 69 in round two and is alone in fourth place at minus-7.
Ochoa hit a spectacular 7-iron approach at the first and kicked in the 2-footer for birdie. That would be the last good thing to happen for a while as Ochoa found trouble at No. 3.
She hit a terrible drive under a marshal's chair and tried to mark her ball but picked it up first. The 'rookie mistake' would be a stroke penalty and, eventually, Ochoa walked off with a double-bogey seven.
Ochoa rallied with back-to-back birdies at seven and eight. At the par-5 10th, she hit a sand wedge to 5 feet to set up her fourth birdie. She added another birdie at the 14th when her 9-iron stopped 15 feet from the stick.
Ochoa tapped in for a birdie at the 16th, ran home a 7-foot birdie putt at 17 and closed with a 30-footer for birdie to join Davies in a share of the lead.
'It was a good round because the way I started with that with that double- bogey early in the day, I really didn't get angry or anything,' said Ochoa, who tied for second last year. 'I just thought there's a lot of holes left and you're going to be fine.'
Davies began her second round on the back nine and sputtered out of the gate with six consecutive pars. At the par-3 16th, Davies missed the green with a 5-iron and could not get up and down for par.
Davies more than atoned for the error with a spectacular 5-iron approach at the par-5 17th. Her second landed 17 feet from the hole and she converted the eagle putt to reach 7 under par for the championship.
At the par-4 18th, Davies missed the fairway on the left side, but was able to get a pitching wedge on her ball. She knocked her approach to 15 feet and holed the birdie putt to make the turn at 2-under-par 34.
Davies parred her first two holes on the front side then hit a wonderful 2-iron to 20 feet at the par-5third. She drained the eagle putt and found herself in the lead at minus-10.
The Englishwoman hit a 7-iron to 10 feet to set up birdie at the par-3 fifth, a hole she has birdied in each of her first two rounds. At the seventh, Davies chipped to 4 feet and sank the birdie putt to reach 12 under par, which topped Kim's record from last year by four.
Davies has not won on the LPGA Tour since the 2001 Wegmans Rochester International. That is not to say that Davies has not visited the winner's circle in other parts of the world.
Since her last win on tour, Davies has collected six worldwide victories in places such as Norway and Australia. She finished atop the Order of Merit last year on the Ladies European Tour and is in great shape to earn a spot on this year's Solheim Cup team.
'I've been playing good golf. It's just when you're not putting the scores on the board on the LPGA, people think you've been not playing well anywhere,' said Davies. ' I just haven't had good results on the LPGA for whatever reason; probably putting and a little lack of confidence over here.'
Se Ri Pak (70), Suzann Pettersen (69), Nicole Castrale (69) and Brittany Lincicome (72) are knotted in fifth place at 5-under-par 139.
Carri Wood (69), Christina Kim (67), Seon-Hwa Lee (69), Tracy Hanson (70) and Karin Sjodin (66) share ninth place at minus-4.
The 36-hole cut fell at 2-over-par 146 and Morgan Pressel, the winner of the Kraft Nabisco Championship two weeks ago, will miss the weekend. She shot an even-par 72 on Friday and missed the cut by a stroke at plus-3.