The 19-year-old Kovtun, who's in just his second year of senior competition, was the only figure skater to attempt two quad jumps — and he landed them both perfectly. He didn't perform a planned triple Axel, but his routine was still solid enough with 85.96 points to take a three-point lead over Hanyu's mistake-filled routine.
China's 18-year-old Yan Han also struggled with his landings, finishing third with 79.21.
Canada's Nam Nguyen is in sixth place heading into the free skate after scoring 72.85 in his short.
In the women's short, Russians Julia Lipnitskaia and Elizaveta Tuktamysheva finished first and second, respectively, well ahead of the field. Lipnitskaia scored 69.56 points and Tuktamysheva 67.99.
Japan's Kanako Murakami was third with 60.44.
Canada's Gabrielle Daleman was fourth with 58.49.
The Cup of China is the third of six stops on the ISU Grand Prix of Figure Skating circuit.