The 20-year-old Kim, winless in two seasons on the LPGA Tour, had an 8-under 136 total on the Blackhawk Country Club course. Fankhauser shot a 68.
"It was really cold this morning," Kim said. "I was just like, `Go out there and do my best and, you know, hopefully I can start (fast),' which I did.
"I have a little lower ball flight, so I think that helps me a little bit with the wind. And if it's not raining, I'm OK with everything, any conditions."
Thirty-nine players shot under par in the first round, but only 17 in the second.
Ochoa, a seven-time winner this season who lost a playoff to Suzann Pettersen last year at Blackhawk, followed her opening 70 with a 68.
"There's no other way to describe it but a really tough day," Ochoa said. "I did make a few bogeys out there and a couple silly mistakes. But at the same time I was really pleased, really happy, especially with the way I finished, making three birdies out of the last four holes. For sure dinner will taste better, and I'm right there where I'd like to be for the weekend."
Angela Stanford was 5 under after a 69, and Pettersen (72), LPGA Championship winner Yani Tseng (72), Kristy McPherson (70) and Charlotte Mayorkas (71) were 4 under.
Kim had four birdies on the front nine, dropped a stroke on par-3 10th and closed with eight straight pars. The 2005 U.S. Girls' Junior champion lost a playoff to Ochoa last season in the Wegmans LPGA.
In her last five starts, she has two top-10 finishes and five top-20s.
"I feel I'm getting there," Kim said. "The competition is really hard and tough. I like to challenge myself. I think it's been fun, and I think I'm going to have more fun."
Bay Area star Paula Creamer, the Samsung World Championship winner Sunday at Half Moon Bay, was even par after a 70. Santa Cruz resident Juli Inkster, the Hall of Famer who won in 1999 and 2000 at Twelve Bridges, shot a 77 to drop to 3 over.
First-round leaders Maria Hjorth and Michele Redman struggled Friday. Hjorth, nearly five months pregnant, followed her opening 66 with an 80, leaving her 2 over. Redman was 3 under after a 75. Fankhauser grew up in Ohio and plated at Ohio State, often playing in frigid, windy conditions.
"I didn't even really think it was cold or windy today," Fankhauser said. "Even though I've been out of school for a few years, it's a nice advantage just to go out in 45-degree weather and think that I've played in 35-degree weather when it's 40-mile-an-hour winds and almost snowing."
Fankhauser missed the cut in 14 of 20 events this year but tied for seventh last month at the Bell Micro LPGA Classic, her first career top-10 finish.
"It's fun," Fankhauser said. "It's better than missing a cut. I don't really care if my name is first or second on the leaderboard. I love the opportunity."