Berrer, ranked 104th, advanced at his hometown, clay-court event to face Agustin Calleri, who rallied to defeat Pablo Cuevas of Uruguay 5-7, 7-5, 6-1.
"I played very well against him,'' Berrer said. "If someone quits, that means you were too strong.''
Second-seeded Richard Gasquet stopped Czech qualifier Lukas Rosol 6-7 (7), 6-2, 6-2, and will play Albert Montanes, who won an all-Spanish duel against Oscar Hernandez 7-6 (4), 6-4.
In a match delayed because of darkness on Tuesday, fifth-seeded Simone Bolelli of Italy defeated Mischa Zverev of Germany 6-7 (6), 6-4, 6-2.
Brian Dabul of Argentina defeated Denis Gremelmayr of Germany 6-3, 5-7, 6-3.
Pliskova, Vinci advance to Prague Open quarterfinals
Lehmann returns to Germany
“Michael Ballack is the key to victory”