River coach Nestor Gorosito's job is on the line after his team's 1-0 defeat at Arsenal followed a 0-0 home draw with Colon last weekend and early elimination in midweek from the Copa Sudamericana, South America's Europa League equivalent.
Boca, who also went out of the Copa Sudamericana to Argentine champions Velez Sarsfield in midweek, have taken five points and River four after five matches.
Boca made a string of defensive mistakes in Sunday's defeat, conceding an early goal to Godoy Cruz when Matias Jara latched on to a weak back pass from Paraguayan defender Julio Cesar Caceres to skip past goalkeeper Roberto Abbondanzieri and score.
Chile midfielder Gary Medel put Boca ahead with his first goal for the club since his loan move from Universidad Catolica, a diving header after keeper Nelson Ibanez had parried midfielder Federico Insua's fierce drive in the 56th.
With Boca pressing for a winner, Godoy Cruz hit them on the break in the final minute, Jara's perfect low ball from the left going between defender Hugo Ibarra and Abbondanzieri to substitute Cristian Chavez who tapped in at the far post.
Not even the presence at the Bombonera of one of Boca's most famous fans, U.S. Open tennis champion Juan Martin del Potro, could lift the team from their present gloom.
Promoted Chacarita Junior's Ricardo Zielinski became the first coach to lose his job this season when by mutual agreement he left with the team bottom with no points.
