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.
Midfielder Andrezinho opened the scoring in the fourth minute from a corner, defender Bolivar added a second after an hour and Giuliano completed the win in stoppage time. Inter substitute Edu was sent off two minutes from time.
Corinthians, who secured top place in Group One last week, beat Colombian champions Independiente Medellin 1-0 in Sao Paulo with a Juan Valencia own goal to amass 16 points from their six matches, the best record in the group phase.
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.
BRAZILIAN QUINTET
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.
They have been pitted against Argentine opponents with San Luis facing holders and Group Three winners Estudiantes and Guadalajara meeting Velez Sarsfield, who topped Group Seven.
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.
The matches will be played over the next two weeks with the quarter-finals scheduled in May before the competition goes into recess for the World Cup.
Ties for the first knockout round of the South American Libertadores Cup (first team at home in first leg):
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)
Matches to be played on April 28 and May 5.
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