The 80th-ranked Zopp raced to a 5-0 lead before the sixth-seeded Spaniard managed to hold serve for the first time.
Garcia-Lopez had an early break in the second set but then lost his serve four times in a row.
Earlier, Martin Klizan of Slovakia defeated Austrian wild card Dominic Thiem 6-1, 3-6, 7-5.
The fifth-seeded Klizan was broken at love while serving for the match at 5-3 but broke Thiem again in the final game of the match.
Attila Balazs of Hungary defeated Martin Fischer of Austria 6-3, 1-6, 7-6 (2) to set up a second-round match against Philipp Kohlschreiber. The top-seeded German, who will play at the London Olympics, had a bye in the opening round of the Austrian clay-court event.