There was another away win for Sao Paulo, who upset 2009 runners-up Cruzeiro in the first leg of their all-Brazilian tie at the Mineirao in Belo Horizonte.
The term Maracanazo was first coined when Uruguay upset Brazil at the giant Maracana stadium in Rio to win the 1950 World Cup.
Universidad de Chile went ahead in the fifth minute, having squandered a very good chance a minute earlier. The Flamengo defenders were unable to control a cross from Eduardo Vargas from the right on the rain-drenched pitch and Uruguay defender Mauricio Victorino rifled the ball into the net.
The Chileans went further ahead in the 25th when midfielder Rafael Olarra met a long, high ball out of defence into the box, rising higher than goalkeeper Bruno to head the ball in.
Striker Adriano, overlooked by Brazil coach Dunga when he named his 23-man World Cup squad on Tuesday, headed Flamengo back into contention six minutes before the interval.
The U were left a man short just before halftime when Chile midfielder Manuel Iturra was sent off for a foul on Willians, his second booking.
However, hardly had the second half begun when The U made it three. Bruno was slow to react to a cross from the left and Uruguay midfielder Alvaro Fernandez beat him at the far post in the 47th minute.
Defender Juan pulled another goal back for the home side one minute from time but The U hung on for victory.
COACH SUSPENDED
Universidad de Chile's Uruguayan coach Gerardo Pelusso had to watch the Maracana match from the stands having been handed a provisional ban by the South American Football Confederation (CSF).
The CSF acted on an official complaint from Alianza Lima following The U's controversial second-round win over the Peruvian side last week.
Alianza believe Pelusso's heated complaints on the touchline persuaded the referee to change his mind and allow the Chileans' stoppage time equaliser when three Universidad players appeared to be offside. The 2-2 draw sent The U through 3-2 on aggregate.
The CSF said it was carrying out an investigation but the result would stand.
Flamengo, South American champions in 1981, and Universidad de Chile met at the group stage when The U won 2-1 at home and held the Brazilians 2-2 in Rio.
The winners of the tie will meet Guadalajara or Paraguay's Libertad. The Mexicans won their home leg 3-0 at the Jalisco in the early hours of Wednesday.
At the Mineirao, striker Dagoberto put three times winners Sao Paulo ahead in the 24th minute and Brazil midfielder Hernanes added the second in the 65th from Fernandao's exquisite backheeled pass.
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