The 34-year-old Quesne made six birdies in Shanghai to put himself in sight of his third European Tour title and first since 2013.
His eight-under total left him one clear of Levy, who looked set to move clear before finding water with his approach at the par-four 16th and double bogeying the hole.
Levy, also 34 and looking for his third European title, followed with another bogey at the par-three 17th but birdied his last to move within one on seven under after a 68, alongside American Peter Uihlein (67).
Thailand’s Kiradech Aphibarnrat, who won last week’s European Tour title in Shenzhen, moved into contention for another victory after firing a 68 early on Friday to move into a tie for fourth.
Italy’s Matteo Manassero matched the Thai’s mark with Wu Ashun (66) and Li Hao-Tong (68) leading the local charge to join the pair at five-under.
It was a welcome return to form for Manassero but he??admitted he was not yet “out of the woods” after a difficult couple of years.
Manassero became the youngest ever winner of the BMW PGA Championship in 2013,??claiming his fourth European Tour title at the age of 20 in a play-off at??Wentworth. Since then he has made just three top-10 finishes and missed the cut in his first five events this season.
“I’m playing very solid golf and I’m glad to have my confidence back and to be shooting some good scores again,” he said. “I like this course and it suits my game.
“I’m not there yet and I don’t want to say I’m completely out of the woods??just yet, but everything is much clearer now and I’m definitely on a much better??path.
“At least I can see the woods are finishing and I am glad to be standing in??this position after two rounds.”