The 24-year-old Yang shot a one-under 69 for a 54-hole total of eight-under-par 202, while world number three Lewis's 69 left her at five under par for the championship.
Yang, who has twice before played in the final pairing at a U.S. Open, will have another golden opportunity on Sunday paired again with Lewis.
"I don't want to think too much ahead, but it would be a great thing to my golf career," Yang said about the possibility of claiming her maiden major.
Chun In-gee, a 20-year-old South Korean, surged to third place with a two-under 68 for a four-under-par 206, one stroke better than Japanese Tour veteran Shiho Oyama, who shot 71 after sliding back with a double-bogey at the par-four fifth.
Four players were grouped at two under par, including last year's winner Michelle Wie, who fired a 68.
Joining Wie on 208, six strokes off the pace, were world number one Park In-bee (70) and fellow Koreans Lee Mi-hyang (68) and Chella Choi, who set a U.S. Women's Open nine-hole record by firing a 29 on the front side on her way to a six-under 64.
Five players had shot 30 for nine holes, the first being Pamela Wright at Indianwood in 1994.
TWO-SHOT SWINGS
Yang enjoyed a four-stroke lead after she birdied the par-five 13th hole to reach nine under par and was threatening to make it a romp.
But a two-shot swing at the par-four 14th tightened the leaderboard as the South Korean bogeyed after a strong chip past the cup, while Lewis birdied to close within two.
A three-putt bogey by Lewis at the 17th hole restored Yang's three-stroke lead.
Earlier, Yang used a two-stroke swing to her advantage, turning a three-shot lead over Lewis into a five-shot bulge as she birdied the first while the American made bogey.
A bogey-birdie exchange in Lewis's favour at the second hole again reversed the effect.
Yang and Lewis, who were both within range of winning their first U.S. Open crown last year, will wage another head-to-head clash paired in Sunday's final round.
Their third-round duel had the feel of match play.
"I felt like I hit some great shots that put a lot of pressure on her, and then she just would respond and hit it right in there with me," said two-times major winner Lewis.
"There were multiple times today that it was iffy who was away. I mean, we were hitting shots on top of each other. In a sense it's frustrating, because you're trying to get closer but you really can't get any closer.
"I think it's great golf. I think we both played really well today given the circumstances, and I expect more of it tomorrow."
(Editing by Gene Cherry)
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