The 24-year-old German player breezed past the qualifier from Kazakhstan 6-3, 6-3.
Argentine Juan Martin Del Potro downed the tournament's fifth seed, Italian Simone Bolelli, 6-3, 3-6, 6-3.
Kohlschreiber will play Del Potro in the quarterfinals Friday.
Also advancing were eighth-seeded Argentine Eduardo Schwank, who beat German wild card Andreas Beck 7-6 (7-5), 6-2, and Czech Jan Hernych, a 7-6 (7-5), 0-6, 7-6 (7-5) winner over Argentine Brian Dabul.
In other quarterfinal matches, No. 2 seed Richard Gasquet of France meets Spaniard Albert Montenes, Schwank plays Hernych and No. 6 Argentine Augustin Calleri encounters German Michael Berrer.