Former world number one Jankovic's hopes of winning her first singles title of the year were ended as she was beaten 6-3 6-3 in the second round of the inaugural WTA International hard-court event.
World number 112 Zheng is 98 places below Jankovic in the rankings, but the Serb had no answer to the underdog as she was second best in a match that lasted an hour and 27 minutes.
Jankovic double-faulted five times and Zheng capitalised to secure a memorable win on home soil.
Zheng claimed the upper hand by breaking in the first game of the match, but the world number 14 responded immediately with a break of her own to level.
Jankovic was unable to gain any momentum, though, and Zheng secured another two breaks to win the first set before taking charge of the second.
A break in the fourth game gave Zheng a 3-1 lead and she broke again to go 5-1 up, then served out the match after Jankovic had given herself some hope by claiming one break back.
Next up for Zheng is a last-eight encounter with Sorana Cirstea, who beat Andrea Hlavackova on Wednesday.
Second seed Peng Shuai must fancy her chances of winning the title in her homeland after seeing off qualifier Elizaveta Kulichkova 6-1 6-2 on Thursday.
World number 22 Peng needed just 63 minutes to cruise into the quarter-finals at the expense of outsider Kulichkova, who was broken on six occasions and managed only one break of her own.
Ajla Tomljanovic now stands in the way of Peng and a place in the semi-finals, while Hsieh Su-wei can look forward to a meeting against Belinda Bencic after she beat Zhang Shuai 3-6 6-3 7-6 (7-5).
Bencic should be fresh heading into that encounter, having progressed courtesy of a walkover as Romina Oprandi had to pull out due to injury.