Fellow Brazilian side Cruzeiro, the South American title favourites, beat Once Caldas 2-1 away in their first leg match in the Colombian city of Manizales.
Wednesday's other matches ended in draws as four times champions Estudiantes found the way to goal blocked by brilliant goalkeeping from Diego Barreto and were held 0-0 by Cerro Porteno in La Plata.
Colombian side Atletico Junior drew 1-1 away to Mexico's Chiapas, whose equaliser was scored by Colombia striker Jackson Martinez.
At Vila Belmiro, teenager Neymar slotted a square ball between two defenders on the edge of the box and Ganso steered it past the diving Francisco Ochoa into the bottom far corner in the 38th minute.
America, who host next week's second leg at the Azteca in Mexico City, had substitute Miguel Layun sent off for a second booking in added time.
Cruzeiro striker Wallyson joined Cerro Porteno's Argentine marksman Roberto Nanni as top scorers in the competition with seven goals apiece when he put his side ahead 18 minutes from time.
The Brazilian side, twice champions and losing finalists to Estudiantes in 2009, went further ahead through Paraguayan substitute Jose Ortigoza with Caldas left back Luis Nunez pulling one back with two minutes remaining.
In La Plata, Barreto, the reserve keeper in Paraguay's 2010 World Cup squad, made a string of good saves, not least when a free-kick from Pablo Barrientos took a deflection and he managed to shift his weight back and make a diving save.
Cerro Porteno had midfielder Rodrigo Burgos sent off four minutes from time for a tackle from behind, his second booking.
"We had seven or eight chances... at least we didn't concede a goal," Estudiantes winger Enzo Perez told Fox Sports.
"We used to be more effective, we'd have two chances and score the goals," added Perez, whose team have not won in six matches in the Argentine league and the Libertadores in the last month.
On Thursday, holders Internacional visit Penarol at the Centenario in Montevideo and Brazilian champions Fluminense host Paraguay's Libertad at the Engenhao in Rio de Janeiro.
