Flamengo, who finished second to Universidad de Chile in Group Eight on Wednesday, had to wait 24 hours to find out if they were among the six best runners-up in the eight groups.
Another Brazilian side, Internacional, beat Deportivo Quito 3-0 at home in Porto Alegre on Thursday to reach the knockout phase as Group Five winners.
With former Brazil World Cup winners Ronaldo and Roberto Carlos in their squad, they hope to mark the club's centenary year with their first South American crown.
Two more Brazilian sides, last-year's runners-up Cruzeiro and three times champions Sao Paulo, also reached the last 16 among the six best second-placed teams to take the country's total to five qualifiers.
Two spots were reserved for Mexico's Guadalajara and San Luis, who were given a bye into this year's knockout phase having had to pull out in 2009 due to the H1N1 epidemic.
In other ties, Universidad de Chile face Alianza Lima, Sao Paulo meet Peruvian champions Universitario, Paraguay's Libertad face Once Caldas of Colombia, Uruguay's Nacional play Cruzeiro and Inter clash with Argentine champions Banfield.
Flamengo (Brazil) v Corinthians (Brazil)
Alianza Lima (Peru) v Universidad de Chile (Chile)
Guadalajara (Mexico) v Velez Sarsfield (Argentina)
Once Caldas (Colombia) v Libertad (Paraguay)
Universitario (Peru) v Sao Paulo (Brazil)
Cruzeiro (Brazil) v Nacional (Uruguay)
San Luis (Mexico) v Estudiantes de La Plata (Argentina)
Banfield (Argentina) v Internacional (Brazil)
