Zverev also defeated Simon at the Rome Masters in May.
"It was nearly identical to the match in Rome," Zverev said. "I had the feeling I could beat him. I tried to keep the ball in play and make him do something because he is a counter puncher."
"He served very well, he never allowed me to get into the match," Kohlschreiber said.
Kubot will face Nicolas Kiefer of Germany, who beat Simon Greul 6-3, 6-4 to reach his first quarterfinal of the year. Second-seeded Nikolay Davydenko eased into the quarterfinals by beating Michael Berrer of Germany 6-3, 6-3.
The Russian is seeking to return to the top 10 after falling out in April for the first time in four years. Davydenko, ranked No. 11, missed much of the first four months of the tour because of various injuries.