The world number 50, top seed for the WTA 125 hard-court event in Nanchang, is a firm favourite to clinch her maiden WTA title after six runners-up finishes, although she had to battle hard to overcome her opponent and book a showdown with Liu Fangzhou.
Peng appeared solid in the opening set, which she won courtesy of a solitary break. She claimed 83 per cent of points on her first serve and saved all three of the break points forced by her opponent.
However, Peng was less commanding in the second set as both players dropped serve on two occasions, and Zheng sustained her hopes of success by claiming the tie-break.
Zheng managed another break in the decider, but gave up her own serve three times as Peng ultimately progressed with a degree of comfort.
She will now take on world number 422 Liu, who was impressive in seeing off fourth seed Luksika Kumkhum.
Teenager Liu edged a first set that saw seven breaks of serve, before triumphing comfortably in the second.