Berlocq broke Zeballos' serve three times.
Earlier Monday, Bulgaria's Grigor Dimitrov was put to the test by 17-year-old Elias Ymer of Sweden, rallying to win 5-7, 6-2, 6-4.
Argentina's Martin Alund also prevailed in a close match against Sweden's Markus Erikson, winning 7-5, 6-7 (5), 7-6 (8) to advance to the second round of the clay-court tournament in Bastad.
Results from the first day of the ATP Swedish Open (x denotes seeding):
Grigor Dimitrov (BUL x5) bt Elias Ymer (SWE) 5-7, 6-2, 6-4
Martn Alund (ARG) bt Markus Eriksson (SWE) 7-5, 6-7 (5/7), 7-6 (10/8)
Carlos Berlocq (ARG) bt Horacio Zeballos (ARG x7) 6-4, 6-3