Bolivian attacker Marcelo Moreno bagged a brace as the Brazilian Serie A champions produced a masterclass in the first leg of their last-16 clash at the Estadio Governador Magalhaes Pinto.
Cruzeiro - seven points clear in Brazil's top flight - went into Wednesday's fixture against Campeonato Alagoana opponents Santa Rita in the midst of a 10-game unbeaten streak in all competitions.
And Marcelo Oliveira's men extended that run thanks to a dominant first half that yielded three goals.
Moreno opened the scoring after eight minutes in Belo Horizonte, looping a header over goalkeeper Jeferson from Alisson's cross.
Centre-back Dede doubled Cruzeiro's lead in the 18th minute, when he headed home from a corner.
Sandro Mendonca's 56th-minute goal gave the second-tier side a surprise 1-0 win in Cuiaba, while it condemned Corinthians to back-to-back defeats.
Corinthians' woes were compounded in the third minute of injury time, when midfielder Ferrugem received his marching orders.
Mineiro were 1-0 victors at Palmeiras on Wednesday, with Luan's glancing header in the 71st minute the difference after Henrique missed a penalty for the home side in the first half.
David Braz and Milan loanee Robinho were both on target in the opening half as Santos upstaged Luiz Felipe Scolari's Gremio 2-0 away from home on Thursday.
The defeat ended Flamengo's four-game winning streak.
Serie B's America RN were 3-0 winners at home to top-flight outfit Atletico PR on Wednesday.
