Futcher and Shin both had six birdies and one bogey to reach 8-under 136 and tie Stanford, who had a 70, on a day temperatures reached the low 90s.
"My putting has been great the last two days so I'm happy to be where I'm at," said Shin, who bogeyed the 13th.
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The second-year LPGA player placed seventh at the season-opening Australian Open and is coming off a tie for ninth in Thailand in Sunday.
"I feel a little bit more confident with my golf game," the South Korean said. "I think Australia helped me a lot. I feel like I know what I'm doing out on the course now.
Futcher's bogey, her first of the tournament, came on the 17th.
"I'm very, very satisfied," the American said. "Went out, made a great putt on No. 1 today for par, and that kind of really just got me settled and I was able after that to hit it pretty close and make a couple of putts."
Stanford started the day with a two-shot lead, but admitted feeling fatigued after her opening 66.
"When I started today, I knew that I didn't quite have that much energy, and so at least I'm starting to recognize it a little earlier in the round," she said. "I felt more tired this morning and the heat didn't help right off the bat."
World No. 1
"I feel I hit the ball pretty good, but my score was terrible and I just - I don't know why," she said. "I didn't make putts and I didn't have much birdie chances actually."
Tseng had two birdies and two bogeys and is tied for 20th at 1 under.
Michelle Wie shot an 81 after a 79 Thursday and was 24 shots behind at 16 over.
The 63-player field in the $1.4 million tournament includes 18 of the top 20 in world rankings.