Internacional lost 3-1 away to Argentina's Banfield and Sao Paulo drew 0-0 with Peruvian champions Universitario in Lima. Both Brazilian teams had players sent off.
A crowd of 72,000 gathered at the Maracana to watch the clash between Brazil's two most popular teams after contrasting results in the group phase.
Corinthians, previously unbeaten, had the best record and Flamengo the worst among the qualifiers for the first knockout round.
Flamengo, who won the trophy in 1981, were a man short from the 37th minute when midfielder Michael was sent off for his second booking after two bad tackles in the space of seven minutes.
A first half in pouring rain gave way to a better second and Brazil's Adriano converted a 64th minute penalty, his first goal for a month, after left back Juan was brought down by Moacir.
It was Flamengo's first match since sacking coach Andrade, who had steered them to the Brazilian title last year, after a poor group performance.
"In our circumstances, I think the victory was excellent. Congratulations to the players who honoured this shirt in a marvellous way," said caretaker coach Rogerio Lourenco, Andrade's former assistant.
TWO-GOAL LEAD
In Buenos Aires, Colombian forward James Rodriguez scored his fifth goal of the competition to put Banfield ahead less than two minutes into the second half. He ghosted in unmarked on the left to shoot from a tight angle past Inter's Argentine keeper Roberto Abbondanzieri.
Inter hit back three minutes later when defender Kleber volleyed into the top corner from the edge of the box, but the goalscorer was sent off seven minutes later for stamping on Banfield playmaker Walter Erviti.
Banfield went ahead again from the free-kick thanks to a goal by midfielder Roberto Battion, which video replays showed was offside.
Tempers flared for a few minutes when Inter's Uruguayan coach Jorge Fossati was hit on the head by an object thrown from the crowd.
Banfield sealed the win 10 minutes from time through Uruguay striker Sebastian Fernandez.
"We beat a great rival. Luckily we got a good difference (in the score) but it's not decisive," Erviti told Fox Sports.
Sao Paulo, three times South American champions, were the more dangerous team at the Monumental in Lima where they hit the post in the first half and had another effort cleared off the line.
They were a man short for the last 25 minutes after forward Richarlyson was shown a straight red card for a nasty tackle on midfielder Rodolfo Espinoza.
Tuesday was a mixed night for Argentine teams on their visits to Mexico where holders Estudiantes beat San Luis 1-0 but Velez Sarsfield lost 3-0 to Guadalajara.
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