An error-prone Cibulkova allowed American Stephens to race into a one set lead before clawing her way back. Having dragged the match into a decider, Cibulkova found her range to close out victory in under two hours.
Cibulkova's first win over Stephens in three years, following defeats in Acapulco and at last year's U.S. Open, earned her a last eight clash with Anastasija Sevastova.
The Latvian advanced with a comfortable 6-3 6-2 victory over Croatia's Donna Vekic.
Sloane Stephens of the United States reacts against Dominika Cibulkova of Slovakia during their Women's Singles 3rd Round match of the 2018 China Open at the China National Tennis Centre on October 3, 2018 in Beijing, China.
Image credit: Getty Images
Former world number one Karolina Pliskova cruised past Aliaksandra Sasnovich of Belarus 6-3 6-4 in a second round clash to set up a meeting with China's Wang Qiang.
Wang won the last meeting between the two players, at last week's Wuhan Open.
Australian Open champion Caroline Wozniacki hardly broke sweat as she felled Croatia's Petra Martic 7-5 6-3.
Up next for Wozniacki is a clash with Estonia's Anett Kontaveit, who has beaten the 28-year-old Dane twice in their previous three matches.
Local hope Zhang Shuai beat Hungary's Timea Babos 6-1 6-2 and faces Wimbledon champion Angelique Kerber next.