The Russian second seed lost the first set before recovering, but still needed an hour and 55 minutes against the world number 42 before prevailing 2-6, 6-4, 7-6 (3).
Her reward is a semi-final place against American Alison Riske, whose victory at the 2014 Tianjin Open remains her only WTA Tour win, but who continued her quest for a repeat by beating home player Han Xinyun 6-3, 6-3.
Kuznetsova is now hot favourite for the title, after Polish top seed Agnieszka Radwanska withdrew from the tournament with a thigh injury after her quarter-final on Thursday.
“It’s the end of the season — I guess everyone is struggling with something,” the world number three said, adding that she decided to pull out to give herself the best chance of recovering before the WTA Finals in Singapore later this month.
Her decision gave China’s Peng Shuai a walkover into Saturday’s semi-final, where she will face Montenegro’s Danka Kovinic, who beat Puerto Rican fifth seed Monica Puig 6-4, 6-3.