Berdych broke Zopp's serve three times in a victory that took only 71 minutes.
The Czech will next face Russia's Mikhail Youzhny and remains in line to qualify for the season-ending ATP World Tour Finals in London.
Top seeded Jo-Wilfried Tsonga, also hoping to qualify for London, advanced with a 6-3, 7-6 (6) win over Go Soeda of Japan.
The Frenchman faces Sergiy Stakhovsky of Ukraine in the quarterfinals after Stakhovsky beat Spain's Feliciano Lopez, 7-6 (5), 7-5.
Marcos Baghdatis of Cyprus advanced when Alejandro Falla of Colombia retired because of a left foot injury while trailing 6-0, 3-0. Baghdatis next faces Lithuania's Ricardas Berankis.
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