The Brazilian outfit came from behind at the Estadio Raimundo Sampaio and Neto Berola's 87th-minute winner gave them the victory over visitors Santa Fe.
Omar Perez had given the Colombians the lead on the hour-mark before it was cancelled out by Jo, while Neto Berola had the final say.
Mineiro are three points clear atop the group after two matches, with Santa Fe (three points), Nacional Asuncion (three) and Zamora (zero) behind them.
Perez looked to have Santa Fe, who were reduced to 10 men when Wilder Medina was sent off on the stroke of half-time, on track for a surprise win in Belo Horizonte with his 60th-minute goal.
But they conceded almost immediately to Jo, before Neto Berola – introduced on 76 minutes – had an impact.
A stunning 11-minute burst early in the second half guided Cerro Porteno to a 3-1 win at home to Lanus in Group Three.
Daniel Guiza opened the scoring a minute after the break for the Paraguayans before Julio Dos Santos struck twice – the second from the penalty spot on 56 minutes.
Argentina's Lanus pulled a goal back through Jorge Ortiz on the hour-mark and they were unable to score again despite the hosts having Angel Romero sent off in the 66th minute.
Flamengo picked up their first points in Group Seven thanks to a 3-1 win over Ecuadorian outfit Emelec in Rio de Janeiro.
Elano, Hernane and Everton netted in the win for Jaime de Almeida's side.
Botafogo stayed top of Group Two after a late goal saw them draw 1-1 at Union Espanola in Santiago de Chile.
Cristian Chavez's 75th-minute effort put the hosts ahead, only for Juan Carlos Ferreyra to equalise with four minutes remaining to snatch a point for the Brazilians.
