Top seed Berdych, the world number six from the Czech Republic, eased past Spain's Roberto Bautista Agut 6-3 6-3 with the help of 11 aces.
Spaniard Lopez, seeded sixth, needed a tie-break in the first set but came through 7-6 (7/5) 6-3 against Go Soeda of Japan.
The other second-round clash was an all-Dutch affair, with Igor Sijsling beating Robin Haase 6-7 (7/9) 6-4 7-6 (7/2).
In first-round action, fifth seed Mikhail Youzhny was a 6-3 6-2 winner over Italy's Paolo Lorenzi.
Denis Istomin beat Korean wildcard Jeong Suk-young 6-3 6-0 while Yen-Hsun Lu of Chinese Taipei beat Russian Evgeny Donskoy 6-3 6-2.