Corinthians, bidding for the title for the first time with former Brazil World Cup winners Ronaldo and Roberto Carlos in their team, went ahead in the 41st minute of the Group One match in Asuncion when Ronaldo tapped in from a corner.
Cerro midfielder Jorge Britez was sent off eight minutes from the end for a violent foul.
Flamengo, who made a lightning visit to Santiago because of fears of another earthquake in Chile, must have wished they had not travelled at all.
Midfielder Felipe Seymour hit the winner in the 55th minute to put "The U" top of Group Eight, a point ahead of the Brazilian champions.
Central and southern Chile were hit by a quake measuring 8.8 on the Richter scale on February 27 that left hundreds dead and massive damage.
Universidad de Chile gave their fans in the 25,000 crowd on Wednesday the joy of victory to distract them from the devastation of the last fortnight.
Striker Eduardo Vargas headed the Chilean side in front two minutes before half time. Flamengo, whose striker Adriano hit the bar early on, equalised through Rodrigo Alvim in the 51st minute but they hardly had time to celebrate before falling behind again to Seymour's strike.
Another Chilean side, Universidad Catolica, secured a point in the same group with a 0-0 draw away to FC Caracas in Venezuela.
