The 23-year-old was two points away from defeat in the third set, but rallied to beat the world number 58 7-5 6-7 7-5.
Edmund will face Croatian qualifier Dusan Lajovic in the last eight.
Lajovic progressed by beating world number eight Grigor Dimitrov 6-4 2-6 6-4.
German second seed Alexander Zverev is the highest ranked player left in Edmund’s side of the draw.
Top seed Juan Martin del Potro beat Russian Karen Khachanov 6-4 7-6 (7-4) and in doing so qualified for the season-ending ATP Finals for the first time since 2013.
Meanwhile, Belgium’s world number 11 David Goffin has ended his season early with an elbow injury which forced him to withdraw from the Japan Open and Shanghai Masters.
Goffin says he has a bone marrow edema, a build-up of fluid, which requires at least one month of recovery.