Hataoka, who earned her third LPGA title at the Kia Classic in Carlsbad, California, in March, had five birdies in her first 12 holes at Kingsmill Resort and bounced back from her lone bogey at the par-four 14th with an eagle at 15.
"I wasn't thinking about where I was going to get a bogey or anything like that, so when it came, it came," Hataoka said. "Then I just cleared it."
She was in the clubhouse on 13-under 200 when Law, who shared the overnight lead with Americans Jennifer Song and Jacqui Concolino, birdied the 18th to join her.
"I've led from the start and I kind of wanted to continue that so that was huge to keep that going," said Law, who finished with six birdies and two bogeys in her four-under 67. "That was really my goal when I teed up on 18."
The leading pair were one stroke in front of Song, who carded a 68 to drop out of the leading group for the first time all week, and Canadian Brooke Henderson, who had eight birdies in her seven-under 64.
It was a further shot back to Spain's Carlota Ciganda, who carded a 68 for 202.
Song said unpredictable winds made for a challenging day.
"The wind was just switching here and there," she said. "It was kind of hard to make decisions with my club."
Whatever the conditions Sunday, Law said, she'll have to stay aggressive if she is to have a shot at a first LPGA title after six top-10 finishes.
"I think you have to keep pushing, you can't sit on anything," Law said. "At no point can you stop making birdies, and you've just got to limit those mistakes."