Cerro, looking to reach their first final when the sides meet again in next week's second leg in Asuncion, have lost only once at home in the competition - to Santos in the group phase.
The Brazilian side, champions in 1962 and 1963 and finalists in 2003, went ahead one minute before half-time when Brazil teenager Neymar jinked his way to the goalline on the left before crossing to the far post where centre-back Edu Dracena's header went in off the bottom of the bar.
Man-of-the-match Neymar looked to have laid on a second goal for the Brazilians three minutes into added-time with another run but substitute Alan Patrick's weak shot was blocked by goalkeeper Diego Barreto.
"Cerro played well. It was a good win for us but in that last attack it could have been better," Edu told Fox Sports.
The Paraguayan side might have equalised from the restart after Edu's goal but goalkeeper Rafael managed to get a foot to striker Fredy Bareiro's diving header.
Neymar proved to be Santos' only real chance of breaking down the Cerro defence and Barreto had to leap to tip the teenager's shot from outside the box over his bar.
"We didn't deserve to lose, it was an even match... Neymar is a player who makes a difference, the move for the goal was his, you need to know how to close him down," said Cerro coach Leonardo Astrada.
