Garcia-Lopez served for the match at 5-1 in the second set but allowed Berrer to come back and force the tiebreaker. Garcia-Lopez also squandered a match point at 5-4 before recovering to win the match at the clay-court tournament.
The 47th-ranked Spaniard next will face French qualifier Stephane Robert, who defeated Thomas Fabbiano of Italy a day earlier.
Also, Rogerio Dutra Silva of Brazil defeated Benjamin Becker of Germany 6-4, 6-1 and Britain's Kyle Edmund beat Daniel Gimeno-Traver of Spain 6-3, 7-5.
Taro Daniel of Japan ousted qualifier Steven Diez of Canada 7-5, 6-1.