Portuguesa raced to a three-goal lead after only 31 minutes against the world club champions, all scored by forward Gilberto, while Corinthians striker Paolo Guerrero had a penalty saved by Lauro.
Corinthians pair Emerson and Alexandro Pato had goals ruled out for offside after the break and Gil was sent off for elbowing an opponent before Wanderson added a fourth for Portuguese with 10 minutes to play.
Corinthians, who have not won in their last eight games and scored only one goal in the process, dropped to 13th in the table with 31 points, only six clear of the relegation zone.
Flamengo needed only 23 minutes to open up a 3-0 lead over Criciuma with two goals from Hernane, the second a penalty, and one from Wallace.
Criciuma goalkeeper Helton Leite was sent off for the foul on Hernane which led to the penalty and his opposite number Felipe was also dismissed in first-half stoppage time for upending Lins.
Daniel Carvalho converted to reduce the deficit but Elias restored Flamengo's three-goal lead late in the second half.
Leaders Cruzeiro won 2-1 at Dunga's Internacional and have 53 points from 24 games, 11 clear of Gremio and Botafogo in second place.
Marcelo Martelotte, Nautico's seventh coach of the year, notched his first win as his side thumped Coritiba, themselves under interim coach Marcelo Serrano, 3-0 to end the longest winless streak in the competition.
However, they are bottom of the table on 14 points, 13 adrift of safety.