The Brazilian Serie A powerhouse were inspired by a Fred brace, plus a late strike from Walter, to ensure they would not have to host Tupi - and progress into the third round of the cup competition.
Copa rules state a two-goal away win in the first leg - at least - ensures automatic progression.
Adrianinho had put Ponte Preta within a goal of automatic progression in the 52nd minute, but Anderson Rosa's equaliser ensured Parana's survival in the cup.
Sao Paulo hit the front on 25 minutes via Ademilson, to put the tie on a knife's edge.
But CRB hit back admirably, with a Tozim penalty on 34 minutes followed by Diego Rosa's winner seven minutes from time.
A Reinaldo Alagoano penalty on 52 minutes, was followed by Marlon Adriano's effort 12 minutes later.
