Former world number three Davydenko leads his head-to-head with Berdych with nine wins in 13 matches, although the Czech world number six has triumphed in two of their last three.
And they will meet again after Davydenko saw off Carballes Baena 6-1 6-4.
The 31-year-old Russian, a two-time semi-finalist in this competition, was far from his best in a low-quality encounter and lost his serve on three occasions, although he countered that by breaking his Spanish opponent six times.
Davydenko's compatriot Dmitry Tursunov will meet top seed David Ferrer next following a 6-3 6-4 win over Denis Istomin, while Latvia's Ernests Gulbis meets home favourite and 12th seed Fernando Verdasco in the second round following a 7-6 (7/4) 6-2 over Radek Stepanek.
Pablo Andujar came through a tight encounter with Grega Zemlja before emerging a 6-7 (8/10) 7-6 (7/3) 6-2 victor, while Spanish wild cards Pablo Carreno-Busta and Albert Montanes gave the fans something to cheer with wins over Robin Haase and Ricardas Berankis respectively.
Ivan Dodig, Andrey Kuznetsov, Paolo Lorenzi and Guillermo Olaso also booked their places in the last 32 today.