The 19th-ranked Russian forced a single service break in each set and denied De Schepper any chances to break back. The French left-hander sent down seven aces but had six double faults.
In the quarterfinals on Friday, Youzhny faces the player he beat in the title match last year, Robin Haase of the Netherlands.
Seventh-seeded Haase had a tougher time in the Swiss mountains beating local wild card Henri Laaksonen 6-4, 1-6, 7-5.
Leading 5-3 in the decider, Haase had his serve broken then wasted three match points in Laaksonen's next service game. Haase finally clinched the match on an error by the 319th-ranked Swiss.
Troicki is playing his first event after serving a one-year suspension for a doping rules violation, which left him ranked No. 847.