Victories of two goals or greater away from home in the first 90 minutes secures automatic progression to the next round in Brazil's cup competition, with the top-flight outfits able to shirk their second-round second legs with comfortable road wins.
Coritiba dismissed Caldense 2-0, gaining a two-goal advantage inside 20 minutes courtesy of goals to Jaja and Robinho at the Estadio Dr Ronaldo Junqueira.
Corinthians beat Nacional AM 3-0 on the road, with Cleber, Paolo Guerrero and Romarinho all getting on the scoresheet.
Also progressing to the third round on Thursday was Santa Rita, who thrashed Potiguar Mossoro 7-2 on aggregate.
After a 2-0 home win in the first leg, Santa Rita were poised to advance, and Potiguar Mossoro did not get within one goal of overhauling the deficit as the visitors piled on the goals.
Santa Rita led at the Nogueirao when Junior Amorim opened the scoring on seven minutes, although Potiguar struck back moments later through Paulo Paraiba.
Micheel reinstated the visitors' three-goal aggregate lead in the 14th minute, only for a Vava penalty making the second leg 2-2 after 36 minutes.
But a second-half barrage, including a Rafael brace and an Alexsandro goal, sent Santa Rita flying into the third round.
There were four second-round first legs played across Wednesday and Thursday that will require second matches, after close results.
Vasco da Gama came from behind to beat Treze on the road 2-1, falling one goal shy of automatic progression.
The Serie B outfit should progress when they return home for the second leg on May 14.
Novo Hamburgo enjoyed a 1-0 home win over J Malucelli, while Cuiaba were held 1-1 at home to Internacional while Gremio Barueri earned a 0-0 draw on the road at Londrina.
In first-round ties, Bahia advanced past Villa Nova 3-1 on aggregate, while Sport Recife won 3-1 away at Brasilia to end their tie after 90 minutes.
Ceara beat Parnahyba 1-0 on the road in their first leg.
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