The Cypriot Baghdatis played at this tournament for the fourth time in his career, but has never been able to reach more than the second round.
Next up for Garcia-Lopez will be the winner of the match between the 9th seed Gilles Simon of France and Fabio Fognini of Italy.
Also through is Russia’s qualifier Igor Andreev after beating the Spanish veteran Juan Carlos Ferrero 6-4 7-6 (4).
Ferrero is currently ranked 49th, but he has been struggling this season so far, only winning one match in the Davis Cup.
Andreev’s next opponent will either be the last week’s BMW Open champion Philipp Kohlschreiber of Germany or the 12th seed Gael Monfils of France.
In the other first round matches, Nikolay Davydenko of Russia defeated the big serving Croatian Ivo Karlovic 7-6 (4) 6-3, American wild card holder Ryan Harrison eliminated the Ukrainian qualifier Sergiy Stakhovsky 7-6 (3) 7-6 (5), 11th seeded Spaniard Nicolas Almagro ousted Colombian qualifier Santiago Giraldo 6-7 (5) 6-3 6-3 and Viktor Troicki of Serbia overcame American Donald Young 6-1 4-6 6-1.
The top seeds Djokovic, Nadal and Federer have a first round bye.