The third-placed Wanderers made it six wins in a row in the Chilean Primera Division to keep the pressure on leaders Universidad Chile, while Colo Colo remain second after their fourth consecutive victory.
But Hector Tapia's men had to do it the hard way at Cobresal's Estadio El Cobre with Paredes converting from the spot, after Rodrigo Urena had dragged down Felipe Flores in the box as the Colo Colo man attempted to get his head to a cross from the left.
Before Paredes could take the penalty, however, Cobresal delayed proceedings for five minutes due to their protests with unused substitute Fabian Cerda shown a red card after disputing the referee's decision from behind the home side's goal, while Rodrigo Urena was also sent off.
Also on Sunday, Deportes Iquique and Nublense played out a 1-1 draw, while Agustin Gonzalez struck in the second half for Union La Calera to secure a 2-2 stalemate at Audax Italiano.
Colo Colo's win took them to 32 points, two adrift of Universidad Chile, who won the Clasico Universitario 3-0 over Universidad Catolica on Saturday.
Patricio Rubio struck in the third minute and with three minutes remaining in the derby in Santiago de Chile, while Matias Corujo scored Universidad de Chile's second goal in the first half.
Wanderers (31 points), who have not lost in the Chilean top tier since August, needed a penalty to defeat O'Higgins 1-0 on Friday with Jorge Luna scoring from the spot in the 67th minute.
Promoted club Barnechea continued their surge up the table with a 1-0 win over Union Espanola, making it four games without a loss, while Palestino trumped Antofagasta 3-1.
Huachipato won 2-0 against Cobreloa and San Marcos played out a scoreless draw with Universidad de Concepcion.