Having claimed a 2-0 win away to ASA last week, Flamengo wrapped up a 4-1 aggregate victory at the Estadio General Silvio Raulino de Oliveira thanks to goals from Elias and Bolivian striker Marcelo Moreno.
Flamengo captain Elias gave the Rio de Janeiro-based club the lead two minutes before half-time when he tapped home from close range but ASA hit back soon after the break with a thumping strike from Osmar.
While a draw would have been enough for Flamengo, the home side claimed victory in the 81st minute after Bruninho stole the ball off an ASA defender and then chipped it to Moreno, who volleyed home at the six-yard box.
Cruzeiro cruised to a 6-0 aggregate victory on Wednesday with a 1-0 triumph over Atletico GO, while Internacional drew 1-1 with America Mineiro to advance 4-2 on aggregate.
Criciuma was the only Brazil Serie A side to be eliminated from the Copa do Brasil after a stunning finish to their second leg against Salgueiro.
Having claimed a scoreless draw away to Salgueiro last week, Criciuma took a 35th-minute lead against the Serie D side through Fabio Ferreira and looked to be heading towards the fourth round until Fabricio Ceara unleashed an unstoppable volley for the visitors with three minutes remaining.
Salgueiro held on for a 1-1 draw and clinched a berth in the next round.
In other Copa do Brasil results, Goias drew 1-1 with ABC to claim a 4-1 triumph over two legs and Luverdense defeated Fortaleza 2-1 to advance after the first leg finished 0-0.