The third-seeded Czech dropped just six first-serve points and saved the only break he faced.
Berdych next faces Milos Raonic, who beat Marton Fucsovics 6-2, 6-4. The seventh-seeded Canadian is going for his first title on grass.
Guido Pella of Argentina beat Indian qualifier Prajnesh Gunneswaran 7-6 (4), 6-3 to set up a quarterfinal against Roger Federer.
Also, fourth-seeded Nick Kyrgios returned from a right elbow injury to beat Maximilian Marterer 6-4, 4-6, 6-3 for a match against Feliciano Lopez. Lopez progressed past Gilles Simon 7-6 (6), 6-4.