Gabriel Graciani notched a brace for Colon, who moved to nine points and second position in the Primera Division table.
The Santa Fe-based club have never won Argentina's top tier of football but after claiming their third consecutive victory on Sunday, Colon are only behind Godoy Cruz on goal difference.
Graciani put Colon in front in the 17th minute at their Estadio Brigadier General Estanislao Lopez, when he ran onto Cristian Sain's pin-point pass over River Plate's defence and then lifted the ball over Marcelo Barovero before being crunched by the visiting goalkeeper.
Colon doubled their lead in the 71st minute when substitute Martin Luque produced a mazy run from the left wing, cutting inside one defender and holding off another marker before converting through Barovero's legs.
River responded almost immediately with Fernando Cavenaghi poking the ball home after a fine run and pass from Manuel Lanzini.
But Colon secured the victory with three minutes left when an unmarked Graciani finished off Luque's cross to the back post.
Colon are one of four teams on nine points, with Godoy Cruz (plus five goal difference), ahead of them, while Estudiantes and San Lorenzo trail the second-placed club from Santa Fe on goals scored.
Velez Sarsfield, Atletico Rafaela and Rosario Central sit in the next three positions with seven points each.
Gonzalo Castellani's hat-trick saw league leaders Godoy Cruz to a convincing 3-0 win over Rosario Central.
Estudiantes lost 1-0 at Boca Juniors on Sunday with Emmanuel Gigliotti scoring the winner for the home side, while San Lorenzo defeated Quilmes by the same scoreline thanks to a goal from Ignacio Piatti.
Velez Sarsfield slumped to a 3-2 loss at Lanus, who had Oscar Benitez score a brace, while Atletico Rafaela were thrashed 4-1 at Newell's Old Boys.
In other matches, All Boys edged Olimpo 1-0, Arsenal beat Racing Club 3-1, Tigre drew 0-0 against Argentinos Juniors and Gimnasia La Plata and Belgrano played out a thrilling 2-2 draw.
