The fifth-seeded Zeballos defeated seven-time French Open champion Rafael Nadal in the final of the VTR Open in Chile just over a week ago.
Expectations were high for him playing at home.
After winning the second-set tiebreaker, Bedene then broke Zeballos in the second game of the deciding set en route to the victory.
"It was my first match since August, I think, on clay. So at the beginning I was confused," Bedene said. "I'm really happy with my performance—first round, first win."
Bedene apologized for beating the hometown favorite at the Buenos Aires Lawn Tennis Club.
"Horacio is my good friend, so I feel sorry for him," Bedene said. "But tennis is tennis and somebody has to win."
No. 2 seed Nicolas Almagro defeated Argentine Guido Pella 6-3, 6-2, continuing his recent success on clay in Latin America.
In 2012, Almagro won on clay in Brazil and was the runner-up in Buenos Aires. In 2011, the Spaniard won twice in Latin America—in Brazil and Buenos Aires—and was the runner-up in Acapulco, Mexico.
"This trip through Latin America has been very good for me in recent years," Almagro said. "But every year is different."
In other first-round matches, No.
Top-seeded David Ferrer of Spain plays in the first round Tuesday against Agustin Velotti.