The country's big two are struggling for form with Boca lucky to salvage a point after being awarded a debatable penalty in the third minute of added time.
At the final whistle, angry words between players appeared to spark the mayhem with television cameras catching some players throwing punches while others tried to calm their team mates and opponents. The fighting continued on the way down the tunnel to the dressing rooms.
Referee Pedro Arganaraz, in charge of only his fourth top flight match, had little impact while trying to separate players and issued no more red cards after sending off Godoy Cruz midfielder Federico Lertora in the 72nd minute.
"This is football, calm down guys," Godoy Cruz coach and former Boca idol Martin Palermo was heard to shout.
"The way we live and feel football today, we often go overboard, we're all responsible. We need more calm and a cool head...otherwise we make this spill over into the stands.
"If the fans see this, we're generating more violence," he told reporters later.
The draw left Boca in fourth place five points behind leaders Newell's Old Boys, whose five-match winning streak was ended by Rosario Central who beat them 2-1 in Sunday's derby.
At River's Monumental stadium, fans lost their patience with coach Ramon Diaz's team and insulted them after striker Rodrigo Mora missed a sitter in the first half and Colombia's Teo Gutierrez blasted a penalty over the bar in the second.
River are 13th, 11 points adrift of Newell's in the "Inicial", first of two championships in the season, having scored only eight goals in 12 matches.