Stark had a two-round total of 10-under 134 on the Qizhong Garden Golf Club course in the LPGA's first return to China since 2019 because of the COVID-19 pandemic.
Two-time defending champion Danielle Kang of the US and Yu Liu of China, who both shot 67 in rainy conditions, were tied for second.
"I think I played a little bit better than yesterday actually because I hit better shots," Stark said. "Obviously didn't make as many putts as I did yesterday, but overall my game felt better."
Stark had her first birdie of the day on the third hole. A missed green on the par-3 seventh led to her only bogey through 36 holes, but she recovered quickly with birdies on 8 and 9.
She closed with two more birdies on 13 and 16 to finish with the first 36-hole lead of her tour career.Â
Stark, who admitted to a confidence boost after her first Solheim Cup start last month in Spain, will play alongside Kang and Yu in the third round.
Yu, whose 67 tied her season-low individual 18-hole score, had a solo birdie on 3 and a bogey on 8 in her first eight holes. But it was five birdies in the next six holes on 9 and 11-14 that brought Liu back up the leaderboard and in contention once again in her home country.
"To be honest, pretty low expectations coming in because I'm not good at playing in the rain, so I knew the forecast was pretty much going to rain all throughout the round, which it did," said Yu, who finished in a tie for ninth in 2018 and a tie for third in 2019 in the event's first two editions.
"So I just feel like - my goal today was just to get through the round without making too much damage. I feel like I did a pretty good job."
Kang's round consisted of seven birdies - including four in her final six holes - and two bogeys. Kang is now 25 under in her last six rounds at the LPGA Shanghai.
"I have hit some good drives. Keep giving myself some good opportunities ... able to hit the second shots and stuff, so game has been feeling good for a little bit," said Kang.
Azahara Munoz, who shot 66, is in a three-way tie for fourth with rookie Yuna Nishimura (67) and Thailand's Pavarisa Yoktuan (68) at 8 under.
Minjee Lee is Australia's best placed player in a 8-way tie for 14th.
The event is the start of a four-tournament Asia swing, with later stops in South Korea, Malaysia and Japan.
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