"I'm happy that I have a chance," Wie said after her 2-over-par 72 on Saturday at Pinehurst No. 2. "I'm happy that I'm in contention. I'm just grateful for another opportunity to get a major championship."
Yang emerged atop the leaderboard late in Saturday's round, when she posted six birdies. A bogey on the final hole dropped her back into a tie with Wie.
The two will play in the final pairing in Sunday's last round. They are locked at 2-under 208.
"I still can't complain," Wie said. "Obviously, there were a couple of shots I wanted back, and I felt I could do better. At the same time, I really grinded out there."
Four golfers, including 53-year-old Juli Inkster, who had a 66, are tied for third, four strokes back.
Yang will be in the tournament's final group for the second time in three years. She was the runner-up in 2012.
"I had that experience quite a lot. I'm pretty calm about it."
No American has won the tournament in four years and Yang said she understands the gallery will be pulling for Wie, who's without a major title.
Wie's four-stroke lead evaporated in part because of a double-bogey from a greenside bunker on No. 11. That began her struggles as she played a three-hole stretch in 4-over.
"Driver got a little shaky on a couple of holes," Wie said. "I went into places I shouldn't have. Just made it really difficult for myself."
Yang had only eight pars Saturday, but it was good enough to move to the top. She saved par from a bunker on the par-4 16th hole. Her four bogeys came on par-4 holes.
The scrutiny is bound to fall on Wie, a Hawaiian who emerged as a prominent female player as a teenager but has yet to secure the big prizes.
Wie said she has the proper mindset as a 54-hole co-leader.
"It's definitely a lot of fun," she said. "I love being in contention. I love feeling nervous on the first tee. I love that every shot really counts. It's exactly why I started playing golf, is to have these opportunities."
All this brought Inkster, the oldest entrant in this year's tournament, back into contention after she posted the tournament's best score at 66. Inkster, who entered the round tied for 28th place, is at 2 over.
Inkster vowed that this will be her 35th and last U.S. Women's Open, even after the third-round charge.
"I just don't play that much anymore," Inkster said. "I still hit the ball relatively good, it's just my concentration and I hit a few loose ones and miss a couple of short putts. You just can't win that way."
Inkster, who turns 54 on Tuesday, is a two-time champion of the U.S. Women's Open, most recently in 2002.
When Inkster made her move Saturday before the leaders had teed off, she built momentum and the crowd continually showed its appreciation. That adoration is likely to grow across the last 18 holes.
"It's nice, especially when you're playing well," Inkster said.
Lexi Thompson threatened Wie's lead first, pulling within one shot by playing the first five holes in 2-under. But a double-bogey 6 on the eighth hole dented the ascent and a double-bogey 5 on the next hole sent her six strokes back when, just moments later, Wie drained a birdie putt on the ninth hole.
The 19-year-old Thompson struggled to a 74, tumbling to 3-over for the tournament and into a seventh-place tie. She declined post-round interview requests.